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California State University, Stanislaus

California State University, Stanislaus (Stanislaus State, Stan State) is a public university in Turlock, Stanislaus County, California. It is part of the California State University system. It was established in 1957 and offers 45 bachelor's degree programs, 17 master's degree programs, one doctoral degree (Doctor of Education), and 6 teaching credentials. Stanislaus State is a Hispanic-serving institution.

History
In 1957, the California State Legislature established what was then called Stanislaus State College as the 15th campus of the CSU system. Because Turlock was better known at the time for its turkeys than its aspirations towards higher education, Clark Kerr highlighted this event in his memoirs as an example of how the state colleges had become vulnerable to pork barrel politics in the state legislature. This was one of several reasons behind the creation of the California Master Plan for Higher Education of 1960.

Classes began on the Stanislaus County Fairgrounds in September, 1960, and the college moved to its current location five years later. The college was first accredited in 1964. It gained university status and its current name in 1986.

In 1974, the university established an extension program at the campus of San Joaquin Delta College in Stockton in neighboring San Joaquin County. In 1998 the Stanislaus State-Stockton Center expanded and moved to its own permanent campus in downtown Stockton.

Sarah Palin's selection as the keynote speaker at Stanislaus State's main fundraising event in 2010 resulted in the most successful fundraiser in the campus's history. It provoked speculation and debate when the university refused to disclose her speaking fee and certified public accountants representing Clendenin Bird & Company from Modesto, California were called in to do an internal audit regarding the investigation. The event was organized by a school foundation.

Academics
Fall freshman statistics

California State University, Stanislaus offers 45 undergraduate programs, 17 master's degree programs and 2 graduate certificate programs, 6 school credential programs and a doctoral degree program in Educational Leadership. Its academic disciplines are clustered within four colleges:
 * College of the Arts, Humanities and Social Sciences
 * College of Business Administration
 * College of Education, Kinesiology and Social Work
 * College of Science

Several individual programs, across the four colleges, have achieved and maintain accreditation by professional accreditation bodies. Stanislaus State's College of Business Administration is accredited by the AACSB. Its Human Resource Management program has the nation's top student testing success rate. In fall 2012, Stanislaus State launched an online Master of Business Administration (MBA) degree program, the first fully online AACSB-accredited MBA program offered in the state of California.

The university library building was originally named for founding president Dr. J. Burton Vasché. The library currently holds over 370,000 volumes, 841 print journal subscriptions, access to 141 electronic databases, and a growing number of electronic journals, video recordings, and compact discs. The University Library also contains a Children's collection, which has more than 5,900 titles of children's literature. The library offers access to more than 70 electronic databases and also contains federal, state, and local documents.

As of fall 2017, the five most popular bachelor's degrees Programs are BS Business Administration, BA Psychology, BA Liberal Studies, BA/BS Biological Sciences, and BA Criminal Justice.

The university has several resources available for students. The Tutoring/Writing Center is located in the Vasche Library and offers individual and group tutoring. Some of the services available include essay planning, organization, development and revision, writing across the curriculum, ESL, and WPST test preparation. The university also has a bookstore that features marble herms by sculptor Andrew Wilson alongside other artwork, as well as a university police department and financial aid office. The New Stanislaus State Student Center is scheduled to open Spring 2020.

Rankings
The 2023 U.S. News & World Report Best Regional Colleges West Rankings ranked Stanislaus 4 on Top Performers on Social Mobility, 9 on Top Public Schools, 12 on for best Colleges for Veterans, and 293 in Nursing (tie).

The 2022 U.S. News & World Report Best Regional Colleges West Rankings ranked Stanislaus 6 on Top Performers on Social Mobility, 12 on Top Public Schools, 14 on for best Colleges for Veterans, and 332 in Nursing (tie).

In 2020, Cal State Stanislaus was ranked 1st by Washington Monthly for "Best Bang for the Buck" out of 215 schools in the U.S. western region.

Athletics
Stanislaus State, in the Division II of the NCAA, competes in the California Collegiate Athletic Association (CCAA). Stanislaus State fields 14 sports for men and women for the fall, winter, and spring seasons. Fall sports for men include soccer and cross country. Fall sports for women are soccer, volleyball and cross country. The winter sport for men is basketball and for women it is basketball and indoor track and field. Spring sports for men include baseball, golf, and track and field. Spring sports for women include softball, track and field, and tennis. Stan State also sponsors a competitive cheer team, which has competed at the NCA National Championships since 2017. Besides both being located in the east of California, but one in the south and the other in the north, Stanislaus and San Bernardino have competed heavily as conference rivals.

Ed & Bertha Fitzpatrick Arena
Ed & Bertha Fitzpatrick Arena (aka Warrior Gym) is a 2,000-seat multi-purpose, built in 1978, which is the home arena for the university's Warriors basketball and volleyball teams. It was also briefly the home of the defunct Big Valley Shockwave of the American Basketball Association. In the 2010–2011 season the name of the basketball arena was changed to Ed & Bertha Fitzpatrick Arena.

Student life
The university has a Hmong Students Association. In 2004 the association and a former member led the Project Ready for School to help children arriving in the United States from a Thai refugee camp for preparing for school.

As of fall 2018 CSU Stanislaus had the third largest enrollment percentage of Mexican Americans in the California State University system.

Greek life – sororities and fraternities
Greek life at CSUS includes:

Alumni

 * Susan Eggman – Currently serving in the California State Senate
 * Nancy Stoyer - Scientist who assisted in the discovery of 5 elements
 * Steve Andrade – Major League Baseball pitcher for the Kansas City Royals
 * Gregorio Billikopf – professor and author
 * Dennis Cardoza – U.S. Representative for California's 18th congressional district
 * Gary Condit (B.A., 1972) – former Congressman from California, initially implicated in the Chandra Levy murder case, before being cleared
 * Leo Dottavio – Reality television personality, actor, and comedian, known for his performance on The Bachelorette Season 14
 * Carrie Henn – Child actress who starred in Aliens
 * Rusty Kuntz – former Major League Baseball outfielder and 1984 World Series Champion; current Kansas City first base coach
 * Rico Oller (1980) – former California State Senator
 * Jasmine Sandlas – Indian-American playback singer, television personality, performer, and songwriter
 * Joe Ryan (baseball) - Baseball pitcher for the Minnesota Twins
 * Robert J. Ulrich (casting director) - Emmy Award-winning casting director, producer and former host of the show The Glee Project
 * Kim Johnston Ulrich - Actor who starred in shows including As the World Turns and Passions

Faculty

 * As'ad AbuKhalil – Professor of Political Science
 * Richard Weikart – Professor Emeritus of History, fellow at the Discovery Institute

title: California State University, Stanislaus


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Wikipedia:Archived articles for deletion discussions/2004 June 3

This page is an archive of the discussion surrounding the proposed deletion of many pages.

This page is kept as an historic record.

The results of these debates were to delete the relevant articles.

Please do not edit this page.

Trollgnaw
4 hits on Google, term idiosyncratic, apparently used by 1 person. Maximus Rex 20:46, 28 May 2004 (UTC)

 * Keep, possibly with a rename - the term may be ideosyncratic, but the concept is real. Mark Richards 21:12, 28 May 2004 (UTC)
 * There already exists troll organization, however some people feel the need to push "Trollgnaw" as a separate page. Maximus Rex 22:45, 28 May 2004 (UTC)
 * Keep as redirect to troll organization. - Hephaestos|§ 22:49, 28 May 2004 (UTC)

 * If I remember correctly, this has gone through VfD and consensus then was to delete. It appears to have been re-created.  RickK 22:58, 28 May 2004 (UTC)
 * precedent as in law does not apply to wikis IMHO; since apparently not all community members saw the former debate; there are multiple edits now; perhaps the article would have survived if renamed? -- Waveguy 03:32, 29 May 2004 (UTC)
 * You are seriously mistaken. Precedent in Wikipedia is that if a page has gone through the VfD process and consensus was to delete, if it is re-created, it is to be deleted on sight.  RickK 19:10, 29 May 2004 (UTC)

 * Delete as idiosyncratic. Only known users of the term are User:Leo Trollstoy and a single anonymous Haligonian. —No-One Jones 03:51, 29 May 2004 (UTC)
 * Delete: idiosyncratic. No need for a redirect. Wile E. Heresiarch 19:15, 29 May 2004 (UTC)
 * No need for a redirect unless people keep insisting on going against consensus and re-creating it, no. - Hephaestos|§ 19:17, 29 May 2004 (UTC)
 * Delete. It's seriously misleading for us to suggest that this is a term in actual use. - Nunh-huh 22:58, 29 May 2004 (UTC)
 * Slashdot-ism, delete. Wyllium 23:46, 29 May 2004 (UTC)
 * Delete; no redirect. Neologism that nobody uses. -Sean 00:18, 30 May 2004 (UTC)
 * Delete. Not commonly used. Andris 22:50, May 31, 2004 (UTC)

Trigintillion

 * Can anyone explain in detail the reason trigintillion was put on Vfd?? 66.32.142.216 23:18, 19 May 2004 (UTC)
 * I think I can help. The following are all, AFA I can see made up names for numbers. They score circa 145 hits on google: Trigintillion - Quindecillion - Tredecillion - Quattuordecillion. Alarmingly there about about 100 more of them, each with more zeros and less use than the last. If we have to have them at all, could we have them on a single page with redircts from the discrete page to the common page. For now could we delete these dubious additions. See http://www.io.com/~iareth/bignum.html for background: "As can be seen, there is neither a single definition for these words nor a consistent means of deriving them ... "Using the rules described above" the author goes on to 'invent' some of the above. --Tagishsimon 23:19, 19 May 2004 (UTC)
 * I had, in fact heard of trigintillion and the decillions up to quattuordecillion before. They're legitimate enough. But I agree on Tagishsimon's proposal. Dpbsmith 23:33, 19 May 2004 (UTC) There is an article on large numbers already, but it doesn't yet have anything like a "list of number words ending in -illion" Dpbsmith 23:34, 19 May 2004 (UTC)
 * These terms may not get very many hits, but whoever entered them did not make up the terms--I saw them at least fifty years ago in Merriam-Webster's Unabridged Dictionary. They are legitimate terms.  They could probably be combined into one page, if that's wanted. Oops, sorry I got this in the wrong order. Rsvk 23:36, 19 May 2004 (UTC)

See also Talk:Sexdecillion/Delete

This page is now preserved as an archive of the debates and is no longer 'live'. Subsequent comments on the issues or the deletions should be placed on other relevant 'live' pages. Please do not edit this page.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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One-loop Feynman diagram

In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected tree diagram by taking two external lines of the same type and joining them together into an edge.

Diagrams with loops (in graph theory, these kinds of loops are called cycles, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the semiclassical contributions.

One-loop diagrams are usually computed as the integral over one independent momentum that can "run in the cycle". The Casimir effect, Hawking radiation and Lamb shift are examples of phenomena whose existence can be implied using one-loop Feynman diagrams, especially the well-known "triangle diagram":

 * [[Image:Triangle diagram.svg]]

The evaluation of one-loop Feynman diagrams usually leads to divergent expressions, which are either due to:

 * zero-mass particles in the cycle of the diagram (infrared divergence) or
 * insufficient falloff of the integrand for high momenta (ultraviolet divergence).

Infrared divergences are usually dealt with by assigning the zero mass particles a small mass λ, evaluating the corresponding expression and then taking the limit $$\lambda \to 0$$. Ultraviolet divergences are dealt with by renormalization.

title: One-loop Feynman diagram


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Overloading (chess)

Overloading (also overworking ) is a chess tactic in which a defensive piece is given an additional defensive assignment which it cannot complete without abandoning its original defensive assignment.

Examples
Krasenkow–Karpov, in the first round of the 2003 Corus chess tournament, reached the diagrammed position with Black to play. As the white rook on f1 is preventing the black queen from giving checkmate by capturing the pawn on f3, Black won immediately with
 * 29... Re1

further pinning the white rook against the king and overloading the rook. White now cannot prevent the black queen from taking the f-pawn: if White tries to protect the rook with 30.Rxe1 or 30.Qc4, then 30...Qxf3. If White sacrifices the rook by playing 30.Kg2, then 30...Rxf1 31.Kxf1 Qxf3+ and loses the other rook with 32...Qxd5.

In Liviu-Dieter Nisipeanu–Anish Giri (see diagram), Giri (Black) played
 * 30... Bxh3

overloading the g2-pawn, as 31.gxh3 is met with 31...f3 32.Re3 Qg5+. After 31.Qc3 Bg4, Nisipeanu resigned.

An overload was also used in Rotlewi versus Rubinstein.

title: Overloading (chess)


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Tree diagram

Tree diagram may refer to:
 * Tree structure, a way of representing the hierarchical nature of a structure in a graphical form

Mathematics and logic

 * Tree diagram (probability theory), a diagram to represent a probability space in probability theory
 * Decision tree, a decision support tool that uses a tree-like graph or model of decisions and their possible consequences
 * Event tree, inductive analytical diagram in which an event is analyzed using Boolean logic
 * Game tree, a tree diagram used to find and analyze potential moves in a game

Linguistics

 * Language tree, representation of a group of languages related through descent from a common ancestor
 * Parse tree, a representation of the syntactic structure of a string according to some formal grammar in linguistics
 * Sentence diagram, a pictorial representation of the grammatical structure of a sentence showing the relationships of phrase structures

Biology

 * Dendrogram, a tree diagram used to illustrate clusters of genes or samples in computational biology
 * Phylogenetic tree, a branching diagram showing the inferred evolutionary relationships among various biological species

Other uses

 * Attack tree, conceptual diagrams showing how a target might be attacked
 * Fault tree diagram, diagram used in deductive failure analysis in various industries
 * Program structure tree, hierarchical diagram that displays the organization of a computer program
 * Treemapping, a method for displaying hierarchical data using nested figures, usually rectangles.

title: Tree diagram


text: Category:Mountain ranges

title: Category:Mountain ranges


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Semiclassical

Semiclassical may refer to:

 * Semiclassical gravity, an approximation to the theory of quantum gravity
 * Semiclassical physics, a theory in which one part of a system is described quantum-mechanically whereas the other is treated classically
 * Beautiful music, a radio format
 * Semi-classical music, a style of music of the Indian subcontinent

title: Semiclassical


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Maria Minna

Maria Minna (born March 14, 1948) is a former Canadian politician who represented the Toronto riding of Beaches—East York in the House of Commons as a member of the Liberal Party from 1993 to 2011.

Background
Minna was born in Pofi, Italy, and moved to Canada with her family at the age of 9. They settled in Toronto, Ontario, in the Christie Pits area. Her father worked in the construction industry and her mother laboured as a factory worker. She is the third eldest of five children, having three sisters and a brother. She attended a vocational high school earning a diploma and started working as a secretary. At age 24 she attended the University of Toronto where she graduated with an Honours B.A. in Sociology. At age 34, she married Robert MacBain, a public relations consultant.

From 1981 to 1992, she served as the volunteer president of COSTI-IIAS (formerly Centro Organizzativo Scuole Tecniche Italiane and the IIAS Italian Immigrant Aid Society), Canada's largest immigrant services organization. She also served as president of the National Congress of Italian-Canadians.

Due in part to her high profile, Minna was appointed to serve on two task forces with the Workers Compensation Board. In 1986 she co-chaired the Task Force on Vocational Rehabilitation and in 1991 she chaired a Task Force on Service Delivery. Both led to significant improvements in the operation of the WCB.

Politics
Minna sought the Liberal nomination for the riding of York West in 1984. She lost to Sergio Marchi. She also tried to get nominated in the riding of York North in 1988 but lost to Maurizio Bevilacqua. The York North nomination fight turned ugly amidst claims of delegate stacking and improper procedures. Minna later appealed the nomination but withdrew the complaint claiming that the appeal process was tainted.

In government
She was elected to parliament in the 1993 election in which the Liberal party won all but one of the 99 Ontario seats. Although the former Liberal candidate ran against her as an independent, she defeated New Democratic Party (NDP) incumbent Neil Young by a margin of two-to-one, thus becoming the first Liberal in history to represent the Beaches area south of the Danforth. As of 2008 she has been re-elected five times easily defeating high-profile candidates such as Peter Tabuns (2004 election, by 7,738 votes) and Marilyn Churley (2006 election, by 2,778 votes; 2008 election, by 4,092 votes ).

On August 3, 1999, Minna was appointed to Cabinet as the Minister of International Cooperation. She held the post until the beginning of 2002. On December 11, 2001, Minna was accused of improperly voting in a municipal by-election. She voted for friend and colleague Gail Nyberg who was running to replace Michael Prue who had been elected to the Provincial government in a September by-election. On advice from municipal officials, Minna cast a ballot even though she didn't live within the ward which occupies the northern half of her riding. According to municipal election rules, anyone who owns or rents a business is allowed to vote. Minna's constituency office was in the ward so that allowed her to cast a ballot. Soon after, Minna was dropped from Cabinet during a ministerial shuffle.

Minna was bitter about the demotion and complained to the Liberal Party's women's caucus that she was told to keep quiet about the issue. She claimed she was "hung out to dry by ambitious individuals...." Later she conceded that the PMO's office had told her that it would be better to wait for the results of the ethics investigation. Initially the ethics counsellor terminated the allegations probe since she was dropped from Cabinet but Minna insisted that it be reopened. She said, "It's my personal credibility that's at stake. It's not the cabinet post." Fellow Liberal MP Sheila Copps who sympathized with Minna's situation was quoted as saying, "The one thing you have in politics is your reputation." The probe was reopened and she was subsequently cleared of any wrongdoing.

During her time in government, Minna has held several leadership roles that have focused on immigration and international relations. In 1994 she was appointed Vice-Chair of the Standing Committee on Human Resources Development and served as Parliamentary Secretary to the Minister of Citizenship and Immigration from 1996 to 1998. In October 2004, Minna was appointed special adviser to the Minister of Foreign Affairs on issues of women, peace and security. In March 2005, Minna led a five-person Parliamentary delegation to assist with the peace process in Sri Lanka.

In opposition
From 2006 to January 2009, Minna was the Official Opposition Critic for the Status of Women. Minna was the Official Opposition Critic for Labour. On May 2, 2011, during the 41st federal election, Minna lost her seat to NDP candidate Matthew Kellway.

Awards
Minna has received several awards recognizing her involvement with the immigrant community. These include the Indo-Canada Chamber of Commerce President's Award (2001), the Permio Italia nel Mondo award for individuals of Italian origin (2001), Results Canada's Outstanding Leadership Award (2002), and the Canada-Sri Lanka Business Council's President's Award (2006).

title: Maria Minna


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Devon Island

Devon Island (ᑕᓪᓗᕈᑎᑦ, ) is an island in Canada and the largest uninhabited island (no permanent residents) in the world. It is located in Baffin Bay, Qikiqtaaluk Region, Nunavut, Canada. It is one of the largest members of the Arctic Archipelago, the second-largest of the Queen Elizabeth Islands, Canada's sixth-largest island, and the 27th-largest island in the world. It has an area of 55247 km2 (slightly smaller than Croatia). The bedrock is Precambrian gneiss and Paleozoic siltstones and shales. The highest point is the Devon Ice Cap at 1920 m which is part of the Arctic Cordillera. Devon Island contains several small mountain ranges, such as the Treuter Mountains, Haddington Range and the Cunningham Mountains. The notable similarity of its surface to that of Mars has attracted interest from scientists.

History and settlement
Robert Bylot and William Baffin were the first Europeans to sight Devon Island in 1616. William Edward Parry charted its south coast in 1819–20, and named it North Devon, after Devon in England, a name which was changed to Devon Island by the end of the 1800s. In 1850, Edwin De Haven sailed up Wellington Channel and sighted the Grinnell Peninsula.

An outpost was established at Dundas Harbour in 1924, and it was leased to Hudson's Bay Company nine years later. The collapse of fur prices led to the dispersal of 52 Baffin Island Inuit families on the island in 1934. It was considered a disaster due to wind conditions and the much colder climate, and the Inuit chose to leave in 1936. Dundas Harbour was populated again in the late 1940s, but it was closed again in 1951. Only the ruins of a few buildings remain today.

Geography
Devon Island is located between Ellesmere Island in the north, Cornwallis Island in the west, and Baffin Island in the south, separated by Lancaster Sound.

Because of its relatively high elevation and its extreme northern latitude, Devon Island supports only a meagre population of muskox and small birds and mammals; the island does support hypolith communities. Animal life is concentrated in the Truelove Lowland area of the island, which has a favourable microclimate and supports relatively lush Arctic vegetation. Temperatures during the brief (40 to 55 days) growing season seldom exceed 10 C, and in winter can plunge to as low as -50 C. With a polar desert ecology, Devon Island receives very little precipitation.

Cape Liddon is an Important Bird Area (IBA) notable for its black guillemot and northern fulmar populations. Cape Vera, another IBA site, is also noted for its northern fulmar population.

Devon Island is also notable for the presence of the Haughton impact crater, created some 39 million years ago when a meteorite about 2 km in diameter crashed into what were then forests. The impact left a crater about 23 km in diameter, which was a lake for several million years.

Devon Island Research Station
The Devon Island Research Station was established in 1960 and it is maintained by the Arctic Institute of North America. It is located in Truelove Lowland, on the northeast coast of Devon Island (75.66667°N, -84.58333°W).

Flashline Mars
The Flashline Mars Arctic Research Station project entered its third season in 2004. In July 2004, Devon Island became the temporary home for five scientists and two journalists, who were to use the Mars-like environment to simulate living and working on that planet. April 2007 through 21 August 2007 was the longest simulation period and included 20 scientific studies.

The Haughton crater is now considered one of the world's best Mars analog sites. It is the summer home to NASA's complementary scientific program, the Haughton–Mars Project. The Island's freezing temperatures, isolation, and remoteness offer scientists matchless research opportunities. Devon Island’s harsh climate and barren terrain endeared it to NASA as the Arctic day and night cycle and restricted communications capabilities offer challenges similar to those presented by long-duration space flights.

HMP has conducted geological, hydrological, botanical, and microbiological studies in this harsh environment since 1997. HMP-2008 was the twelfth field season at Devon Island.

In 2007, fossils of the seal ancestor Puijila darwini were found on the island.

On July 16, 2013, the Canadian Space Agency assigned Canadian astronaut Jeremy Hansen to a secondment with the Centre for Planetary Science and Exploration of the University of Western Ontario at Haughton Crater in preparation for a potential future crewed exploration of Mars, the Moon or the asteroids.

title: Devon Island


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Semiclassical physics

In physics, semiclassical refers to a theory in which one part of a system is described quantum mechanically, whereas the other is treated classically. For example, external fields will be constant, or when changing will be classically described. In general, it incorporates a development in powers of Planck's constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from physical optics to geometric optics.

History
Max Planck was the first to introduce the idea of quanta of energy in 1900 while studying black-body radiation. In 1906, he was also the first to write that quantum theory should recover the classical mechanics at some limit, particularly when Planck constant h tends to zero. With this idea he showed that Planck's law for thermal radiation leads to the Rayleigh–Jeans law, the classical prediction (valid for large wavelength).

Instances
Some examples of a semiclassical approximation include:

 * WKB approximation: electrons in classical external electromagnetic fields.
 * semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity).
 * quantum chaos; quantization of classical chaotic systems.
 * magnetic properties of materials and astrophysical bodies under the effect of large magnetic fields (see for example De Haas–Van Alphen effect)
 * quantum field theory, only Feynman diagrams with at most a single closed loop (see for example one-loop Feynman diagram) are considered, which corresponds to the powers of Planck's constant.

title: Semiclassical physics


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Bank Mandiri

PT Bank Mandiri (Persero) Tbk or Bank Mandiri, headquartered in Jakarta, is the largest bank in Indonesia in terms of assets, loans and deposits. Total assets as of 2022, were 1.992 Trillion rupiah (around US$133 Billion). As of 2022, Bank Mandiri is the largest bank in Indonesia by total assets.

As of December 2022, the bank had 2,364 branches spread across three different time zones in Indonesia and 7 branches abroad, about 13,027 Automatic Teller Machines (ATMs), and 11 subsidiaries, such as: Mandiri Sekuritas, Mandiri Tunas Finance, AXA Mandiri Financial Services, Bank Mandiri Taspen, and Mandiri AXA General Insurance.

Pre-merger
Bank Mandiri is the result of the merger made by Indonesian government from four older government-owned banks that failed in 1998. Those four banks were Bank Bumi Daya, Bank Dagang Negara, Bank Ekspor Impor Indonesia, and Bank Pembangunan Indonesia. During the amalgamation and reorganisation, the government reduced the number of branches by 194 and the number of personnel from 26,600 to 17,620.

Bank Bumi Daya and Bank Ekspor Impor Indonesia was previously merged in 1965 by the Indonesian government under Guided Democracy into Bank Negara Indonesia (BNI) umbrella, 1968: The Indonesian government then reorganized the banks in 1968 as the New Order government took place.

 * Bank Bumi Daya (BBD) started in 1959, when the government nationalized Nationale Handelsbank's operations in Indonesia as a part of boycott on Dutch companies amid both nation's dispute over Western New Guinea, and from them the government created Bank Umum Negara ("State General Bank"). In 1964, during Konfrontasi, the government nationalized Chartered Bank's operations in Indonesia and merged them into Bank Umum Negara; the British overseas bank had first entered Indonesia in 1863 when it opened an agency in Batavia (now Jakarta). In 1965 the government brought Bank Umum Negara into BNI, renaming it Bank Negara Indonesia Unit IV (BNI IV), but in 1968 BNI IV became an independent bank again with the name Bank Bumi Daya.
 * Bank Ekspor Impor Indonesia (BankExim, "Export Import Bank of Indonesia") was created in 1960 as the Indonesian government nationalized the Indonesian operations of Nederlandsche Handel-Maatschappij. The bank then merged into BNI by the government in 1965 and became Bank Negara Indonesia Unit II (BNI II). In 1968, the government split BNI II into two parts, with the BNI Unit II Export-Import Division becoming BankExim, which specialised in trade finance.
 * Bank Dagang Negara (BDN, "State Trading Bank") was established in 1960 from the nationalization of Escomptobank. Escomptobank NV, previously Nederlandsch Indische Escompto Maatschappij until 1949, was established in Batavia in 1857.
 * Bank Pembangunan Indonesia (Bapindo, "Development Bank of Indonesia") had its root from Bank Industri Negara (BIN, "State Industrial Bank"), which was established in 1951. The bank was aimed to finance priority sectors, such as plantations, industry and mining. In 1960, the Indonesian government established Bapindo and merged BIN into it. Bapindo specialised in medium and long-term financing of manufacturing, tourism and transportation. In 1986, Bapindo expanded into general commercial banking.

Merger and later history
In 1998, the government merged BBD, BDN, BankExim and Bapindo to create Bank Mandiri to restructurize some state-owned banks to manage impacts of financial crisis at the time. Bank Mandiri was established on 2 October 1998, and the merged banks operated effectively as a single bank starting on 31 July 1999. The name Mandiri (Indonesian for "self-reliant" or "independent") was coined by President B. J. Habibie during his presidency, with the hope that the bank could become a self-reliant bank and encourage the people, especially who need microfinancing, to also become self-reliant.

In 2004, the bank opened a branch in Dili, East Timor and a representative office in Shanghai, China.

Consumer banking

 * 1) Mandiri Savings:
 * 2) * Mandiri Saving Account
 * 3) * Mandiri Business Saving
 * 4) * Mandiri Plan Saving
 * 5) * Mandiri Hajj Saving
 * 6) * Mandiri Foreign Currency Saving
 * 7) Mandiri Current account
 * 8) * Mandiri Current Account
 * 9) Mandiri DepositMandiri Deposit
 * 10) * Mandiri Foreign Currency Deposit
 * 11) Mandiri Debit
 * 12) * Mandiri Debit
 * 13) Mandiri Prepaid
 * 14) * GazCard
 * 15) * Indomaret Card
 * 16) * E-toll Card
 * 17) Mandiri credit card
 * 18) * Mandiri Visa
 * 19) * Mandiri Mastercard
 * 20) * Mandiri JCB
 * 21) Mandiri consumer loan
 * 22) * Mandiri KPR
 * 23) * Mandiri KPR Multiguna
 * 24) * Mandiri personal loan
 * 25) * Mandiri Mitrakarya
 * 26) * Mandiri Tunas KPM
 * 27) Mandiri Priority Services
 * 28) * Mandiri Priority Services
 * 29) * Merchant Relations Program
 * 30) Investment Products
 * 31) * Mutual funds
 * 32) * ORI & Sukuk Ritel
 * 33) Bancassurance
 * 34) * Mandiri Investasi Sejahtera
 * 35) * Mandiri Jiwa Sejahtera
 * 36) * Mandiri Rencana Sejahtera
 * 37) Retail Brokerage Service
 * 38) * Retail Brokerage
 * 39) Consumer Banking Treasury (CBT)
 * 40) * Consumer Banking Treasury

International

 * Bank Mandiri Singapore Branch, operate under wholesale bank licence granted by Monetary Authority of Singapore
 * Bank Mandiri Hong Kong Branch
 * Bank Mandiri Cayman Islands Branch
 * Bank Mandiri Dili Branch
 * Bank Mandiri Shanghai Branch
 * Bank Mandiri (Europe) Limited, located in London, UK. Subsidiary of PT Bank Mandiri (Persero) Tbk.

Principal

 * Mandiri Sekuritas, at Capital Market Awards 2011, PT Mandiri Sekuritas got 3 awards from 9 awards (Marketing Net, the Best Bond Emiten, and the Best Stock Exchange member)
 * AXA Mandiri Financial Services
 * Bank Sinar Harapan Bali (BSHB) (now Bank Mandiri Taspen or Bank Mantap)
 * Mandiri Tunas Finance
 * Mandiri Utama Finance
 * Mandiri AXA General Insurance
 * Asuransi Jiwa InHealth Indonesia (now Mandiri InHealth)

Awards
Based on mystery shopper method done by surveyor, in 2011 Bank Mandiri got average value 91.23 percent, a first time for a bank got more than 90 percent over 15 years survey. Bank Mandiri got Service Excellence Award for 4 times consecutives and got The Most Consistent Bank for 2 times.

title: Bank Mandiri


text: Talk:Worship and Tribute

title: Talk:Worship and Tribute


text:
Edward Follansbee Noyes

Edward Follansbee Noyes (October 3, 1832 – September 4, 1890) was a Republican politician from Ohio. Noyes served as the 30th governor of Ohio.

Biography
Noyes was born in Haverhill, Massachusetts. He was orphaned at the age of three and was raised in New Hampshire by his grandfather and a guardian. At the age of thirteen, he was apprenticed to the printer of The Morning Star, a religious newspaper published in Dover, New Hampshire. He remained an apprentice for over four years until he left to enter an academy in Kingston, New Hampshire. He graduated from Dartmouth College in 1857 (4th in a class of 57 students), then moved to Cincinnati, Ohio, and attended the Cincinnati Law School.

Noyes served in the Union Army during the Civil War. He helped organize the 39th Ohio Infantry, and was rewarded with a commission as its first major on July 27, 1861. Within a few months, he had become the regiment's colonel.

Noyes married Margaret W. Proctor at Kingston, New Hampshire in February, 1863, while on leave from the army.

He was severely wounded in his ankle in a skirmish at Ruff's Mill on July 4, 1864, during the Atlanta Campaign and, as a result, had his left leg amputated. Three months later, Maj. Gen. Joseph Hooker assigned Noyes, who was still recuperating and using crutches, to the command of Camp Dennison near Cincinnati, breveted him as a brigadier general. Noyes commanded the post until April 22, 1865, when he resigned to become city solicitor.

He was elected in October 1866 as the probate judge of Hamilton County.

He was elected to the governorship in 1871, besting another former Union Army officer, Col. George W. McCook, by more than twenty thousand votes. He served one two-year term between 1872–74, pushing for stricter coal mine inspection laws and promoting fish conservation. He lost re-election in 1873 by 817 votes, 50.1% - 49.9%.

In 1874, he was appointed an Ohio Commissioner of the Centennial Exposition in Philadelphia

He later served as Rutherford B. Hayes's Minister to France from 1877 to 1881, a patronage reward for his strong support of his fellow Buckeye soldier during Hayes' presidential campaign.

He died on September 4, 1890, in Cincinnati, Ohio. He was buried in Spring Grove Cemetery in Cincinnati, Ohio.

title: Edward Follansbee Noyes


text:
West Humboldt Range

The West Humboldt Range is a short mountain range in the western Great Basin in northwestern Nevada in the United States.

Geography
The mountain range runs for approximately 40 mi southwest to northeast in northern Churchill County and southern Pershing County. The southwest end of the range is approximately 60 mi ENE of Reno.

The range separates the lower course and terminus-(Humboldt Lake) of the Humboldt River and the Humboldt Sink on the northwest side from the expansive Carson Sink on the south and southeast side. Interstate 80 follows the course of the Humboldt along the northwest side of the range. During the last ice age, the range stood along the shore of Lake Lahontan, the prehistoric shorelines and beaches of which are visible along the sides of the range.

Few peaks in the range are named; one of the few with an official name is Topog Peak in northern Churchill County, near the southwestern end of the range.

History
In 1905 the Saurian Expedition, led by John C. Merriam and financed by Annie Alexander, explored the Triassic limestones of the range, discovering 25 specimens of Ichthyosaur.

title: West Humboldt Range


text:
Richard Conte

Nicholas Peter Conte (March 24, 1910 – April 15, 1975), known professionally as Richard Conte, was an American actor. He appeared in more than 100 films from 1939 through the 1970s, including I'll Cry Tomorrow, Ocean's 11, and The Godfather.

Early life
Richard Conte was born Nicholas Peter Conte on March 24, 1910 in Jersey City, New Jersey, the son of Italian-Americans Julia (Fina), a seamstress, and Pasquale Conte, a barber. He graduated from William L. Dickinson High School in Jersey City.

Conte worked as a truck driver, messenger, shoe salesman, and singing waiter before starting his acting career. He was discovered by actors Elia Kazan and John Garfield during his job at a Connecticut resort, which led to Conte finding stage work.

He eventually earned a scholarship to study at the Neighborhood Playhouse in New York City, where he became a standout actor.

Conte was a Republican who campaigned for Dwight Eisenhower during the 1952 presidential election. He was Catholic.

Stage
He made his film debut under the name Nicholas Conte in Heaven with a Barbed Wire Fence (1939) at 20th Century Fox. He played Tony, a hobo who meets up with Joe (Glenn Ford who was also making his film debut) and Anita (Jean Rogers). The three of them make their way west hopping trains. They are later joined by Professor B (Raymond Walburn).

He made his Broadway debut in My Heart's in the Highlands (1939) for the Group Theatre. Also for the Group, he was in Clifford Odets' Night Music (1940). He performed in the road company of Golden Boy.

On Broadway, he was in Heavenly Express (1941) and Walk Into My Parlor (1941). He was a hit in Jason (1942) then was he Family (1943).

During World War II, Conte served in the United States Army, but he was discharged because of eye trouble.

20th Century Fox
In May 1943, Conte signed a long-term contract with 20th Century Fox, changing his name to Richard Conte. His first Fox film was Guadalcanal Diary (1943), where he was billed fourth.

He followed it with another war drama, The Purple Heart (1944), directed by Lewis Milestone; he was billed second, beneath Dana Andrews.

Conte had a smaller part in Captain Eddie (1945), a biopic about Eddie Rickenbacker, and played an Italian POW in A Bell for Adano (1945).

Conte had the star role in A Walk in the Sun (1945), another war film for Milestone, and he was teamed again with Andrews.

Stardom
Fox promoted Conte to top billing with the film noir The Spider (1945). Although a B film for the studio, it was successful enough to establish Conte in film noir.

He had supporting roles in Somewhere in the Night (1946), directed by Joseph Mankiewicz, and the spy film 13 Rue Madeleine (1946), directed by Henry Hathaway.

Conte was borrowed by Enterprise Productions for The Other Love (1947) with Barbara Stanwyck and David Niven. Back at Fox, he was in Hathaway's crime drama Call Northside 777 (1948) as the prisoner whose innocence is proved by James Stewart.

Conte was teamed with Victor Mature in Cry of the City (1948). MGM borrowed him for Big Jack (1949), then he did House of Strangers (1949) with Edward G. Robinson, playing Max Monetti, a lawyer who defends his father (Robinson) against government charges of banking irregularities and goes to prison for jury tampering.

Conte was top billed in Thieves' Highway (1949), directed by Jules Dassin, and co-starred with Gene Tierney in Otto Preminger's film noir Whirlpool (1950).

Universal
Conte signed a contract with Universal Pictures, and he starred in some crime films: The Sleeping City (1950); Hollywood Story (1951), directed by William Castle; and The Raging Tide (1951).

After doing The Fighter (1952) for United Artists, he returned to Universal for The Raiders (1952).

Conte went to Warner Bros to co-star with Anne Baxter and Ann Sothern in The Blue Gardenia (1953) directed by Fritz Lang. Back at Universal, Conte was in Desert Legion (1953). He made Slaves of Babylon (1953) for Sam Katzman at Columbia. Conte started guest starring on TV shows such as Medallion Theatre, Ford Television Theatre, and General Electric Theater.

Bill Broidy
In 1953, Conte signed a contract with Bill Broidy to make six films over three years, and he would be paid 25% of the profits. The first was the crime drama Highway Dragnet (1954), based on a story by Roger Corman, and he then went to England to make Mask of Dust (1954) for Hammer Films director Terence Fisher. He was going to direct The Wolf Pack for Broidy, but it was not made.

Back in the U.S., Conte did The Big Combo (1955) for Cornel Wilde's company; New York Confidential (1955) for producer Edward Small; and The Big Tip Off (1955) for Broidy.

Conte went to England for Little Red Monkey (1955), RKO for Bengazi (1955), and Warners for a Korean War movie Target Zero (1955).

Conte broke out of B movies with the second lead in I'll Cry Tomorrow (1955), an MGM biopic about Lillian Roth starring Susan Hayward. Conte and director Daniel Mann announced they would make Play by Play, but it was not made.

Columbia
Conte made a series of films for Columbia. He co-starred with Judy Holliday in Full of Life (1956), played the lead in The Brothers Rico (1957), and had supporting roles in This Angry Age (1957) and They Came to Cordura (1959).

Television
He continued to guest on TV shows like The 20th Century-Fox Hour and The Twilight Zone ("Perchance to Dream") and played the lead in a TV adaptation of The Gambler, the Nun and the Radio (1960). He had his first regular TV role in The Four Just Men (1959–1960).

Conte supported Frank Sinatra in Ocean's 11 (1960) but then focused on TV: Alfred Hitchcock Presents, Bus Stop, Naked City, Checkmate, Frontier Circus, The DuPont Show of the Week, The Untouchables, Alcoa Premiere, Going My Way, Kraft Mystery Theater, 77 Sunset Strip, The Reporter, Kraft Suspense Theatre and Arrest and Trial.

He had a supporting role in Who's Been Sleeping in My Bed? (1963), Circus World (1964) and The Greatest Story Ever Told (1965) (playing Barabbas) and the lead in The Eyes of Annie Jones (1964) for Robert L. Lippert. After Synanon (1965), he had the lead in Stay Tuned for Terror (1965), shot in Argentina.

Conte had a supporting role in Assault on a Queen (1966), and he was one of several stars in Hotel (1967). In 1966, Conte landed a supporting role in the short-lived CBS sitcom The Jean Arthur Show.

He appeared as Lieutenant Dave Santini in two crime films with Frank Sinatra: Tony Rome (1967) and Lady in Cement (1968). He also did Sentenza di morte (1968).

In 1968, he released his only film as a director, Operation Cross Eagles, in which he also starred.

Conte's later performances include The Bold Ones: The Lawyers, The Challengers (1970), and The Name of the Game (1970).

The Godfather
Conte had one of his memorable performances in The Godfather (1972) as Don Barzini. He was at one time also considered for the title role, Don Vito Corleone, a role performed by Marlon Brando.

The success of the film led to Conte being cast in a series of "mob" roles: Murder Inferno (1973), The Big Family (1973), Pete, Pearl & the Pole (1973), My Brother Anastasia (1973), The Violent Professionals (1973), No Way Out (1973) with Alain Delon, Anna, quel particolare piacere (1973), Shoot First, Die Later (1974) and Violent Rome (1975). He did the horror films Evil Eye (1975), A Diary of a Murderess (1975) and Naked Exorcism (1975).

Family
Conte was married to actress Ruth Storey, with whom he adopted a son, film editor Mark Conte. In 1950, Conte and Storey were living at 1366 San Ysidro Drive in Beverly Hills. They divorced in 1963. He married his second wife, Shirlee Colleen Garner (1935-2014), in 1973; they remained married until Conte's death. His grandson is National Football League free safety Chris Conte. Chris is the son of Mark Conte.

Death
On April 3, 1975, Conte suffered a massive heart attack and a stroke. He was taken to UCLA Medical Center where the staff worked for eight hours to keep him alive. He was put in intensive care and died on April 15. He is buried in Westwood Memorial Park in Los Angeles.

Selected filmography

 * Heaven with a Barbed Wire Fence (1939) as Tony
 * Guadalcanal Diary (1943) as Captain Davis
 * The Purple Heart (1944) as Lieutenant Angelo Canelli
 * Captain Eddie (1945) as Private John Bartek
 * A Bell for Adano (1945) as Nicolo (Italian POW)
 * The Spider (1945) as Chris Conlon
 * A Walk in the Sun (1945) as Private Rivera
 * 13 Rue Madeleine (1946) as Bill O'Connell
 * Somewhere in the Night (1946) as Mel Phillips
 * The Other Love (1947) as Paul Clermont
 * Call Northside 777 (1948) as Frank W. Wiecek
 * Cry of the City (1948) as Martin Rome
 * Big Jack (1949) as Dr. Alexander Meade
 * House of Strangers (1949) as Max Monetti
 * Thieves' Highway (1949) as Nick Garcos
 * Whirlpool (1950) as Dr. William 'Bill' Sutton
 * The Sleeping City (1950) as Fred Rowan, aka Fred Gilbert
 * Hollywood Story (1951) as Larry O'Brien
 * The Raging Tide (1951) as Bruno Felkin
 * The Fighter (1952) as Felipe Rivera
 * Riders of Vengeance (1952) as Jan Morrell
 * The Blue Gardenia (1953) as Casey Mayo
 * Desert Legion (1953) as Crito Damou / Omar Ben Khalif
 * Slaves of Babylon (1953) as Nahum
 * Highway Dragnet (1954) as Jim Henry
 * Mask of Dust (1954) as Peter Wells
 * The Big Combo (1955) as Mr. Brown
 * New York Confidential (1955) as Nick Magellan
 * The Big Tip Off (1955) as Johnny Denton
 * Little Red Monkey (1955) as Bill Locklin
 * Bengazi (1955) as John Gillmore
 * Target Zero (1955) as Lieutenant Tom Flagler
 * I'll Cry Tomorrow (1955) as Tony Bardeman
 * Full of Life (1956) as Nick Rocco
 * The Brothers Rico (1957) as Eddie Rico
 * This Angry Age (The Sea Wall) (1957) as Michael
 * They Came to Cordura (1959) as Corporal Milo Trubee
 * The Twilight Zone (1959) as Edward Hall
 * Ocean's 11 (1960) as Anthony Bergdorf
 * Pepe (1960) as Richard Conte
 * Alfred Hitchcock Presents (1961) (Season 7 Episode 8: "The Old Pro") as Frank Burns
 * The Untouchables  (1961) (Season 2 Episode 15: "The Organization") as Arnie Seeger
 * The Untouchables  (1962) (Season 4 Episode 3: "The Chess Game") as Ira Bauer
 * Naked City (1962) (Season 3 Episode 17: "One of the Most Important Men in the Whole World") as Phil Clifford
 * Who's Been Sleeping in My Bed? (1963) as Leonard Ashley
 * The Eyes of Annie Jones (1964) as David Wheeler
 * Circus World (1964) as Aldo Alfredo
 * Arrest and Trial (1964) (Season 1 Episode 26: "Tigers Are for Jungles) as Paul Dunnell
 * The Greatest Story Ever Told (1965) as Barabbas
 * Synanon (1965) as Reid Kimble
 * Strange Invasion also Extraña invasión and Stay Tuned for Terror (1965) as Steven Jameson
 * Assault on a Queen (1966) as Tony Moreno
 * Hotel (1967) as Detective Dupere
 * Tony Rome (1967) as Lieutenant Dave Santini
 * Death Sentence (1968) as Diaz
 * Operation Cross Eagles (1968) as Lieutenant Bradford (also directed)
 * Lady in Cement (1968) as Lieutenant Dave Santini
 * Explosion (1969) as Dr. Philip Neal
 * The Challengers (TV movie) (1970) as Ritchie
 * The Godfather (1972) as Don Emilio Barzini
 * Il Boss (Murder Inferno) (1973) as Don Corrasco
 * The Big Family (1973) as Don Antonio Marchesi
 * My Brother Anastasia (1973) as Alberto 'Big Al' Anastasia
 * The Violent Professionals (1973) as Padulo
 * Pete, Pearl & the Pole (1973) as Bruno
 * Tony Arzenta (Big Guns) (1973) as Nick Gusto
 * Anna, quel particolare piacere (1973) as Riccardo Sogliani
 * Shoot First, Die Later (1974) as Mazzanti
 * Evil Eye (1975) as Dr. Stone
 * La encadenada (A Diary of a Murderess) (1975) as Alexander
 * Violent Rome (1975) as Lawyer Sartori
 * The Godfather Saga (1977) as Don Emilio Barzini
 * Un urlo dalle tenebre (Naked Exorcism) (1975) as Exorcist

title: Richard Conte


text:
Talk:Friedrich Hölderlin

Untitled
Removed material that is copyright violation (typos and all) of http://www.kirjasto.sci.fi/holderli.htm

RodC 02:00, 3 Jun 2004 (UTC)

The grammar in the work section is pretty bad. It's a little hard to understand what is meant. Someone should set about cleaning it up jordan 15:01, 11 June 2006 (UTC)

WikiProject class rating
This article was automatically assessed because at least one article was rated and this bot brought all the other ratings up to at least that level. BetacommandBot 11:43, 27 August 2007 (UTC)

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 04:01, 10 November 2007 (UTC)

Needs rewrite
Added some on the "rediscovery" of Hölderlin in the 20th century, his influence and on modern editions. The article as it stood really gave no idea why Hölderlin is one of the most revered figures of German poetry, and one of its most intensely discussed classics.Strausszek (talk) 23:44, 21 April 2009 (UTC)

Musical settings
There has been contention in recent edits about additions of musical settings, as to how to establish that a composition after a text by Hölderlin is notable and worth mentioning on this page. It has been proposed that notability is defined by the fact that the work in question has its own Wikipedia page (as opposed to only its composer). This would entail removing a fair amount of content. Is there a consensus on this topic that could result in a coherent set of content? Musiktheaterpedia (talk) 16:15, 19 December 2023 (UTC)

title: Talk:Friedrich Hölderlin


text:
Talk:Juan Pablo Montoya

"Connie Freydell" listed at Redirects for discussion
An editor has asked for a discussion to address the redirect Connie Freydell. Please participate in the redirect discussion if you wish to do so. SSSB (talk) 11:00, 22 January 2020 (UTC)

Importance of British Grand Prix and Italian Grand Prix
We know those ones are the older grands Prix on formula one calendar, however they are not considered the marquee events of Formula one officially (although in the mind of many the form the "classics" of the formula one calendar: British at silverstone, Italian at monza, Belgian at spa, the old german grand prix at the ring, the japanese at Suzuka. This particular driver did not win all of those).

The Long Beach, and the Indy500 are marquee events for Indycar, but really f1 has only the one marquee event, the monaco gp.

I think the italian, and British Grands prix references should be removed from the lead as they are not widely recognizable as belonging to the "top" races in the world. 181.51.32.187 (talk) 18:24, 29 April 2020 (UTC)

 * The interesting thing about Montoya (What defines him as a driver) is that he managed to succeed on both sides of the Atlantic, something this article completely FAILS to clarify. Montoya is often remembered only because of his 7 wins in F1. That's so unfair!,  only 6 years of his career.
 * People in Europe are always thinking that only de FIA championships, and races are important. So Scott Dixon, or Helio Castroneves are not good drivers because they didn't race on F1? because they raced in Long Beach and not in Silverstone? under this logic Jenson Button is a better driver than Scott Dixon? no way! Dale Earnhardt doesn't even exist in your "European World"?

 * Montoya cannot even count all his important wins together.. For example an F1 driver wins 20 races over 15 years on F1.. the 20 wins are considered important, his achievements..

 * well.. lets see.. Montoya's  case, he has these accomplishments:

 * These to me are his important wins (Not counting podiums = do the Podiums and you'll have something very interesting)
 * 7 F1 wins
 * 14 Champcar/IndyCar wins
 * 6 GrandAm/IMSA wins
 * 2 Nascar (sprint Cup) wins
 * that's 29 important races (I would add his victory at lmp2 pro am at lemans, that makes 30 important wins, no only 7.  30 mayor races)

 * on these wins you even have:
 * 1 Mónaco gpx
 * 2 Indy 500 wins
 * 3 Daytona 24h wins
 * 1 lemans 24h win (lmp2 pro am)
 * that makes 7 iconic victories

 * Not to mention... 3 Championships
 * 1 Champcar/Indy Championship
 * 1 Imsa weathertech Championship
 * 1 F2/F3000 Championship
 * plus
 * 1 Oval Championship (Indy)

 * other wins
 * 10 F2/F3000 wins
 * 1 Nascar Nationwide win

 * then..

 * in Europe
 * 7 wins F1
 * 10 wins F3000/F2
 * 1 win at lemans (lmp2 pro am)
 * 1 F2/F3000 Championship
 * 2 times 3rd on F1 Championship

 * In America
 * 14 Champcar/IndyCar wins
 * 6 GrandAm/IMSA wins
 * 2 Nascar (sprint Cup) wins
 * 1 Champcar/Indy Championship
 * 1 Imsa weathertech Championship
 * 1 Oval Championship (Indy)
 * 1 Time runner-up Indy Championship

 * with
 * 2 Indy 500 wins
 * 3 Daytona 24h wins 181.55.155.218 (talk) 05:42, 4 September 2021 (UTC)
 * f1 has only the one marquee event, the monaco gp - not true. The Monaco GP is the equivilant of the Indy 500. The British and Italian Grands Prix are the equivilant of Long Beach. I completely reject the notion that this article is Euro-centric. The majority of this article covers what he did in American. The majority of the infobox covers his career in American and the majority of the lead covers his career in America. I'm not saying it's perfect - but to suggest it is Euro-centric is absurd. SSSB (talk) 09:03, 4 September 2021 (UTC)

Lemans 2021
His accomplishments of this year 2021 at lmp2 pro am, are diminished, listed as only on the general classification, but they were 1st on their class at lemans. And they still have the chance to win the lmp2 pro am championship. 181.55.155.218 (talk) 03:12, 1 September 2021 (UTC)
 * We show his general classification result, class result and sub-class results in Juan Pablo Montoya. Or do you have an issue with another part of the article? SSSB (talk) 07:02, 1 September 2021 (UTC)

 * You have a table where you listed his category as LMP2 Pro Am, and he finished 10th at Lemans? why? on this category he finished 1st not 10th. If you deliberately specify the "Category" and "Sub Class" then specify the correct result. 181.55.155.218 (talk) 12:03, 8 September 2021 (UTC)
 * Ah, this is a case of the table incorrectly idnetifying his class as LMP2 Pro-Am, where as this is a sub-category. The class (keeping consistency with above rows) is simply LMP2. I have now corrected this. SSSB (talk) 12:11, 8 September 2021 (UTC)

 * SSSB you are completely Biased. you just dont want to accept he won on lmp2 pro am Category/Sub class, and you find any way to put an asterisk on his win. I can send you a picture of the podium if you want. 181.55.155.218 (talk) 12:16, 8 September 2021 (UTC)
 * I'm not dening anything, nor am I biased. Don't make claims you can't back-up. I am going out of my way to compromise here, rather than just say "this is the accpeted convention". The table shows he was 15th in the overall classification, 10th in LMP2 and a note indicates he won LMP2 Pro-Am. I've made an attempt at a compromise at Juan Pablo Montoya. Or would you like another pair of rows for the LMP2 Pro-Am sub-class. SSSB (talk) 14:18, 8 September 2021 (UTC)

 * https://en.wikipedia.org/wiki/François_Perrodo  like this article there are like 150 more where the drivers are listed on the tables as winners "1st" with a yellow square meaning "first" I will make a compilation for you SSSB so you please be so gentle to correct all those articles that are wrong and not according to your standard of adjusting to the number of arrival in the race. After all we all want that Wikipedia is "Objective" and not for re-writing history... I will come again here with the list of articles to review. 181.55.155.218 (talk) 17:49, 12 September 2021 (UTC)

 * eben you have a table in the Championship he is competing at the moment (LMP2 pro/am) where he has been on the podium of his subclass in all races in 2021. Spa he was 3rd you listed him as 7th, Portimao he was 2nd you listed him as 8th even the race initials are wrong on your table. Monza, he was 2nd, you listed him as 6th Leman he was 1st you listed him as 10th. So your tables for the WEC are deliberately edited on your own criteria. He is competing on lmp2 pro am for your information. 181.55.155.218 (talk) 18:09, 12 September 2021 (UTC)
 * He is competing in both LMP2 class and the LMP2 Pro-Am sub-class (i.e. he could be declared outright LMP2 Champion). The results table show his results for the LMP2 classification and this is made very clear in the class column (where it says "LMP2", not "LMP2 Pro-Am"). With regards to your François Perrodo example, allpying that here would produce: Special:Permalink/1044059288. Because the class is LMP2, LMP2 Pro-Am is a sub-class. That it why I suggested doing this: Special:Permalink/1044059911 in the last sentence of my edit on 14:18, 8 September 2021 (UTC) (my last comment before this one). SSSB (talk) 10:39, 13 September 2021 (UTC)

do whatever you want man.. it's a lost case with you. 181.55.155.218 (talk) 05:05, 16 September 2021 (UTC)

please add a single table to lmp2 pro.am to be fair. 181.55.155.218 (talk) 10:00, 25 September 2021 (UTC)

 * A dedicated table would be WP:undue, but I will add a row to the existing table for LMP2 Pro-Am. SSSB (talk) 10:13, 25 September 2021 (UTC)

"Tennis injury" urban legend?
I seem to recall reading somewhere that JPM actually injured himself in a dirtbike crash, and that the "tennis injury" was merely a cover given as the official story. 194.207.183.182 (talk) 14:38, 25 October 2022 (UTC)

Career results
I'm surprised that there's no career results section on his page...Anybody on it? 24.201.79.253 (talk) 13:17, 31 January 2024 (UTC)

title: Talk:Juan Pablo Montoya


text:
Inherit

Inherit or Inherited may refer to:

 * Inheritance, passing on of property after someone's death
 * Heredity, passing of genetic traits to offspring
 * Inheritance (object-oriented programming), way to compartmentalize and re-use computer code
 * Inherit (album), 2008 work by the group Free Kitten
 * Inherited (script), name for dependent script characters, like diacritics (ISO code Zinh)

title: Inherit


text:
WKB approximation

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly.

The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method. Other often-used letter combinations include JWKB and WKBJ, where the "J" stands for Jeffreys.

Brief history
This method is named after physicists Gregor Wentzel, Hendrik Anthony Kramers, and Léon Brillouin, who all developed it in 1926. In 1923, mathematician Harold Jeffreys had developed a general method of approximating solutions to linear, second-order differential equations, a class that includes the Schrödinger equation. The Schrödinger equation itself was not developed until two years later, and Wentzel, Kramers, and Brillouin were apparently unaware of this earlier work, so Jeffreys is often neglected credit. Early texts in quantum mechanics contain any number of combinations of their initials, including WBK, BWK, WKBJ, JWKB and BWKJ. An authoritative discussion and critical survey has been given by Robert B. Dingle.

Earlier appearances of essentially equivalent methods are: Francesco Carlini in 1817, Joseph Liouville in 1837, George Green in 1837, Lord Rayleigh in 1912 and Richard Gans in 1915. Liouville and Green may be said to have founded the method in 1837, and it is also commonly referred to as the Liouville–Green or LG method.

The important contribution of Jeffreys, Wentzel, Kramers, and Brillouin to the method was the inclusion of the treatment of turning points, connecting the evanescent and oscillatory solutions at either side of the turning point. For example, this may occur in the Schrödinger equation, due to a potential energy hill.

Formulation
Generally, WKB theory is a method for approximating the solution of a differential equation whose highest derivative is multiplied by a small parameter $ε$. The method of approximation is as follows.

For a differential equation $$ \varepsilon \frac{d^ny}{dx^n} + a(x)\frac{d^{n-1}y}{dx^{n-1}} + \cdots + k(x)\frac{dy}{dx} + m(x)y= 0,$$ assume a solution of the form of an asymptotic series expansion $$ y(x) \sim \exp\left[\frac{1}{\delta}\sum_{n=0}^{\infty} \delta^n S_n(x)\right]$$ in the limit $δ → 0$. The asymptotic scaling of $δ$ in terms of $ε$ will be determined by the equation – see the example below.

Substituting the above ansatz into the differential equation and cancelling out the exponential terms allows one to solve for an arbitrary number of terms $S_{n}(x)$ in the expansion.

WKB theory is a special case of multiple scale analysis.

An example
This example comes from the text of Carl M. Bender and Steven Orszag. Consider the second-order homogeneous linear differential equation $$ \epsilon^2 \frac{d^2 y}{dx^2} = Q(x) y, $$ where $$Q(x) \neq 0$$. Substituting $$y(x) = \exp \left[\frac{1}{\delta} \sum_{n=0}^\infty \delta^n S_n(x)\right]$$ results in the equation $$\epsilon^2\left[\frac{1}{\delta^2} \left(\sum_{n=0}^\infty \delta^nS_n'\right)^2 + \frac{1}{\delta} \sum_{n=0}^{\infty}\delta^n S_n''\right] = Q(x).$$

To leading order in ϵ (assuming, for the moment, the series will be asymptotically consistent), the above can be approximated as $$\frac{\epsilon^2}{\delta^2} S_0'^2 + \frac{2\epsilon^2}{\delta} S_0' S_1' + \frac{\epsilon^2}{\delta} S_0'' = Q(x).$$

In the limit $δ → 0$, the dominant balance is given by $$\frac{\epsilon^2}{\delta^2} S_0'^2 \sim Q(x).$$

So $δ$ is proportional to ϵ. Setting them equal and comparing powers yields $$\epsilon^0: \quad S_0'^2 = Q(x),$$ which can be recognized as the eikonal equation, with solution $$S_0(x) = \pm \int_{x_0}^x \sqrt{Q(x')}\,dx'.$$

Considering first-order powers of $ϵ$ fixes $$\epsilon^1: \quad 2 S_0' S_1' + S_0'' = 0.$$ This has the solution $$S_1(x) = -\frac{1}{4} \ln Q(x) + k_1,$$ where $k_{1}$ is an arbitrary constant.

We now have a pair of approximations to the system (a pair, because  $S_{0}$ can take two signs); the first-order WKB-approximation will be a linear combination of the two: $$y(x) \approx c_1 Q^{-\frac{1}{4}}(x) \exp\left[\frac{1}{\epsilon} \int_{x_0}^x \sqrt{Q(t)} \, dt\right] + c_2 Q^{-\frac{1}{4}}(x) \exp\left[-\frac{1}{\epsilon} \int_{x_0}^x\sqrt{Q(t)} \, dt\right].$$

Higher-order terms can be obtained by looking at equations for higher powers of $δ$. Explicitly, $$ 2S_0' S_n' + S''_{n-1} + \sum_{j=1}^{n-1}S'_j S'_{n-j} = 0$$ for $n ≥ 2$.

Precision of the asymptotic series
The asymptotic series for $y(x)$ is usually a divergent series, whose general term $δ^{n} S_{n}(x)$ starts to increase after a certain value $n = n_{max}$. Therefore, the smallest error achieved by the WKB method is at best of the order of the last included term.

For the equation $$ \epsilon^2 \frac{d^2 y}{dx^2} = Q(x) y, $$ with $Q(x) <0$ an analytic function, the value $$n_\max$$ and the magnitude of the last term can be estimated as follows: $$n_\max \approx 2\epsilon^{-1} \left| \int_{x_0}^{x_{\ast}} \sqrt{-Q(z)}\,dz \right|, $$ $$\delta^{n_\max}S_{n_\max}(x_0) \approx \sqrt{\frac{2\pi}{n_\max}} \exp[-n_\max], $$ where $$x_0$$ is the point at which $$y(x_0)$$ needs to be evaluated and $$x_{\ast}$$ is the (complex) turning point where $$Q(x_{\ast}) = 0$$, closest to $$x = x_0$$.

The number $n_{max}$ can be interpreted as the number of oscillations between $$x_0$$ and the closest turning point.

If $$\epsilon^{-1}Q(x)$$ is a slowly changing function, $$\epsilon\left| \frac{dQ}{dx} \right| \ll Q^2, ^{\text{[might be }Q^{3/2}\text{?]}}$$ the number $n_{max}$ will be large, and the minimum error of the asymptotic series will be exponentially small.

Application in non relativistic quantum mechanics
The above example may be applied specifically to the one-dimensional, time-independent Schrödinger equation, $$-\frac{\hbar^2}{2m} \frac{d^2}{dx^2} \Psi(x) + V(x) \Psi(x) = E \Psi(x),$$ which can be rewritten as $$\frac{d^2}{dx^2} \Psi(x) = \frac{2m}{\hbar^2} \left( V(x) - E \right) \Psi(x).$$

Approximation away from the turning points
The wavefunction can be rewritten as the exponential of another function $S$ (closely related to the action), which could be complex, $$\Psi(\mathbf x) = e^{i S(\mathbf{x}) \over \hbar},   $$ so that its substitution in Schrödinger's equation gives:

$$i\hbar \nabla^2 S(\mathbf x) - (\nabla S(\mathbf x))^2 = 2m \left( V(\mathbf x) - E \right),$$

Next, the semiclassical approximation is used. This means that each function is expanded as a power series in $ħ$. $$S = S_0 + \hbar S_1 + \hbar^2 S_2 + \cdots $$ Substituting in the equation, and only retaining terms up to first order in $ℏ$, we get: $$(\nabla S_0+\hbar \nabla S_1)^2-i\hbar(\nabla^2 S_0) = 2m(E-V(\mathbf x)) $$ which gives the following two relations: $$\begin{align} (\nabla S_0)^2= 2m (E-V(\mathbf x)) = (p(\mathbf x))^2\\ 2\nabla S_0 \cdot \nabla S_1 - i \nabla^2 S_0 = 0 \end{align}$$ which can be solved for 1D systems, first equation resulting in:$$S_0(x) = \pm \int \sqrt{ \frac{2m}{\hbar^2} \left( E - V(x)\right) } \,dx=\pm\int p(x) \,dx    $$and the second equation computed for the possible values of the above, is generally expressed as:$$\Psi(x) \approx C_+ \frac{ e^{+ \frac i \hbar \int p(x)\,dx} }{\sqrt{|p(x)| }} + C_- \frac{ e^{- \frac i \hbar \int p(x)\,dx} }{\sqrt{|p(x)| }} $$

Thus, the resulting wavefunction in first order WKB approximation is presented as,

In the classically allowed region, namely the region where $$V(x) < E$$ the integrand in the exponent is imaginary and the approximate wave function is oscillatory. In the classically forbidden region $$V(x) > E$$, the solutions are growing or decaying. It is evident in the denominator that both of these approximate solutions become singular near the classical turning points, where $E = V(x)$, and cannot be valid. (The turning points are the points where the classical particle changes direction.)

Hence, when $$E > V(x)$$, the wavefunction can be chosen to be expressed as:$$\Psi(x') \approx C \frac{\cos{(\frac 1 \hbar \int |p(x)|\,dx} + \alpha) }{\sqrt{|p(x)| }} + D \frac{ \sin{(- \frac 1 \hbar \int |p(x)|\,dx} +\alpha)}{\sqrt{|p(x)| }}  $$and for $$V(x) > E$$,$$\Psi(x')    \approx \frac{ C_{+} e^{+    \frac{i}{\hbar}  \int |p(x)|\,dx}}{\sqrt{|p(x)|}} + \frac{ C_{-} e^{- \frac{i}{\hbar} \int |p(x)|\,dx} }{ \sqrt{|p(x)|} }. $$The integration in this solution is computed between the classical turning point and the arbitrary position x'.

Validity of WKB solutions
From the condition:$$(S_0'(x))^2-(p(x))^2 + \hbar (2 S_0'(x)S_1'(x)-iS_0''(x)) = 0 $$

It follows that: $\hbar\mid 2 S_0'(x)S_1'(x)\mid+\hbar \mid i S_0''(x)\mid \ll \mid(S_0'(x))^2\mid +\mid (p(x))^2\mid $

For which the following two inequalities are equivalent since the terms in either side are equivalent, as used in the WKB approximation:

$$\begin{align} \hbar \mid S_0''(x)\mid \ll \mid(S_0'(x))^2\mid\\ 2\hbar \mid S_0'S_1' \mid \ll \mid(p'(x))^2\mid \end{align}   $$

The first inequality can be used to show the following:

$$\begin{align} \hbar \mid S_0''(x)\mid \ll \mid(p(x))\mid^2\\ \frac{1}{2}\frac{\hbar}{|p(x)|}\left|\frac{dp^2}{dx}\right| \ll |p(x)|^2\\ \lambda \left|\frac{dV}{dx}\right| \ll \frac{|p|^2}{m}\\ \end{align}   $$

where $|S_0'(x)|= |p(x)|   $  is used and $\lambda(x) $  is the local de Broglie wavelength of the wavefunction. The inequality implies that the variation of potential is assumed to be slowly varying. This condition can also be restated as the fractional change of $E-V(x) $ or that of the momentum $p(x) $, over the wavelength $\lambda $ , being much smaller than $1 $.

Similarly it can be shown that $\lambda(x) $ also has restrictions based on underlying assumptions for the WKB approximation that:$$\left|\frac{d\lambda}{dx}\right| \ll 1 $$which implies that the de Broglie wavelength of the particle is slowly varying.

Behavior near the turning points
We now consider the behavior of the wave function near the turning points. For this, we need a different method. Near the first turning points, $x_{1}$, the term $$\frac{2m}{\hbar^2}\left(V(x)-E\right)$$ can be expanded in a power series, $$\frac{2m}{\hbar^2}\left(V(x)-E\right) = U_1 \cdot (x - x_1) + U_2 \cdot (x - x_1)^2 + \cdots\;.$$

To first order, one finds $$\frac{d^2}{dx^2} \Psi(x) = U_1 \cdot (x - x_1) \cdot \Psi(x).$$ This differential equation is known as the Airy equation, and the solution may be written in terms of Airy functions, $$\Psi(x) = C_A \operatorname{Ai}\left( \sqrt[3]{U_1} \cdot (x - x_1) \right) + C_B \operatorname{Bi}\left( \sqrt[3]{U_1} \cdot (x - x_1) \right)= C_A \operatorname{Ai}\left( u \right) + C_B \operatorname{Bi}\left( u \right).$$

Although for any fixed value of $$\hbar$$, the wave function is bounded near the turning points, the wave function will be peaked there, as can be seen in the images above. As $$\hbar$$ gets smaller, the height of the wave function at the turning points grows. It also follows from this approximation that:

$$\frac{1}{\hbar}\int p(x) dx = \sqrt{U_1} \int \sqrt{x-a}\, dx = \frac 2 3 (\sqrt[3]{U_1} (x-a))^{\frac 3 2} = \frac 2 3 u^{\frac 3 2}$$

Connection conditions
It now remains to construct a global (approximate) solution to the Schrödinger equation. For the wave function to be square-integrable, we must take only the exponentially decaying solution in the two classically forbidden regions. These must then "connect" properly through the turning points to the classically allowed region. For most values of $E$, this matching procedure will not work: The function obtained by connecting the solution near $$+\infty$$ to the classically allowed region will not agree with the function obtained by connecting the solution near $$-\infty$$ to the classically allowed region. The requirement that the two functions agree imposes a condition on the energy $E$, which will give an approximation to the exact quantum energy levels.The wavefunction's coefficients can be calculated for a simple problem shown in the figure. Let the first turning point, where the potential is decreasing over x, occur at $$x=x_1 $$ and the second turning point, where potential is increasing over x, occur at $$x=x_2 $$. Given that we expect wavefunctions to be of the following form, we can calculate their coefficients by connecting the different regions using Airy and Bairy functions.

$$\begin{align} \Psi_{V>E} (x) \approx A \frac{ e^{\frac 2 3 u^\frac{3}{2}}}{\sqrt[4]{u}} + B \frac{ e^{-\frac 2 3 u^\frac{3}{2}} }{\sqrt[4]{u}} \\ \Psi_{E>V}(x) \approx C \frac{\cos{(\frac 2 3 u^\frac{3}{2} - \alpha ) } }{\sqrt[4]{u} } + D \frac{ \sin{(\frac 2 3 u^\frac{3}{2} - \alpha)}}{\sqrt[4]{u} }\\

\end{align} $$

First classical turning point
For $$U_1 < 0$$ ie. decreasing potential condition or $$x=x_1 $$ in the given example shown by the figure, we require the exponential function to decay for negative values of x so that wavefunction for it to go to zero. Considering Bairy functions to be the required connection formula, we get:

$$\begin{align} \operatorname{Bi}(u) \rightarrow -\frac{1}{\sqrt \pi}\frac{1}{\sqrt[4]{u}} \sin{\left(\frac 2 3 |u|^{\frac 3 2} - \frac \pi 4\right)}    \quad \textrm{where,} \quad u \rightarrow -\infty\\ \operatorname{Bi}(u) \rightarrow \frac{1}{\sqrt \pi}\frac{1}{\sqrt[4]{u}} e^{\frac 2 3 u^{\frac 3 2}} \quad \textrm{where,} \quad u \rightarrow +\infty \\ \end{align} $$

We cannot use Airy function since it gives growing exponential behaviour for negative x. When compared to WKB solutions and matching their behaviours at $$\pm \infty $$, we conclude:

$$B=-D=N $$, $$A=C=0 $$ and $$\alpha = \frac \pi 4 $$.

Thus, letting some normalization constant be $$N $$, the wavefunction is given for increasing potential (with x) as:

$$\Psi_{\text{WKB}}(x) = \begin{cases} -\frac{N}{\sqrt{|p(x)|}}\exp{(-\frac 1 \hbar \int_{x}^{x_1} |p(x)| dx )} & \text{if }  x < x_1\\ \frac{N}{\sqrt{|p(x)|}} \sin{(\frac 1 \hbar \int_{x}^{x_1} |p(x)| dx - \frac \pi 4)} & \text{if } x_2 > x > x_1 \\ \end{cases}   $$

Second classical turning point
For $$U_1 > 0$$ ie. increasing potential condition or $$x=x_2 $$ in the given example shown by the figure, we require the exponential function to decay for positive values of x so that wavefunction for it to go to zero. Considering Airy functions to be the required connection formula, we get:

$$\begin{align} \operatorname{Ai} (u)\rightarrow \frac{1}{2\sqrt \pi}\frac{1}{\sqrt[4]{u}} e^{-\frac 2 3 u^{\frac 3 2}} \quad \textrm{where,} \quad u \rightarrow + \infty \\ \operatorname{Ai}(u) \rightarrow \frac{1}{\sqrt \pi}\frac{1}{\sqrt[4]{u}} \cos{\left(\frac 2 3 |u|^{\frac 3 2} - \frac \pi 4\right)}    \quad \textrm{where,} \quad u \rightarrow -\infty\\ \end{align} $$

We cannot use Bairy function since it gives growing exponential behaviour for positive x. When compared to WKB solutions and matching their behaviours at $$\pm \infty $$, we conclude:

$$2A=C=N'  $$, $$D=B=0 $$ and $$\alpha = \frac \pi 4 $$.

Thus, letting some normalization constant be $$N' $$, the wavefunction is given for increasing potential (with x) as:

$$\Psi_{\text{WKB}}(x) = \begin{cases}

\frac{N'}{\sqrt{|p(x)|}} \cos{(\frac 1 \hbar \int_{x}^{x_2} |p(x)| dx - \frac \pi 4)} & \text{if } x_1 < x < x_2 \\ \frac{N'}{2\sqrt{|p(x)|}}\exp{(-\frac 1 \hbar \int_{x_2}^{x} |p(x)| dx )}  & \text{if } x > x_2\\ \end{cases}$$

Common oscillating wavefunction
Matching the two solutions for region $$x_1<x<x_2 $$, it is required that the difference between the angles in these functions is $$\pi(n+1/2)$$ where the $$\frac \pi 2$$ phase difference accounts for changing cosine to sine for the wavefunction and $$n \pi$$ difference since negation of the function can occur by letting $$N= (-1)^n N'  $$. Thus: $$\int_{x_1}^{x_2} \sqrt{2m \left( E-V(x)\right)}\,dx = (n+1/2)\pi \hbar ,$$ Where n is a non-negative integer. This condition can also be rewritten as saying that:
 * The area enclosed by the classical energy curve is $$2\pi\hbar(n+1/2)$$.

Either way, the condition on the energy is a version of the Bohr–Sommerfeld quantization condition, with a "Maslov correction" equal to 1/2.

It is possible to show that after piecing together the approximations in the various regions, one obtains a good approximation to the actual eigenfunction. In particular, the Maslov-corrected Bohr–Sommerfeld energies are good approximations to the actual eigenvalues of the Schrödinger operator. Specifically, the error in the energies is small compared to the typical spacing of the quantum energy levels. Thus, although the "old quantum theory" of Bohr and Sommerfeld was ultimately replaced by the Schrödinger equation, some vestige of that theory remains, as an approximation to the eigenvalues of the appropriate Schrödinger operator.

General connection conditions
Thus, from the two cases the connection formula is obtained at a classical turning point, $$x=a $$:

$$ \frac{N}{\sqrt{|p(x)|}} \sin{\left(\frac 1 \hbar \int_{x}^{a} |p(x)| dx - \frac \pi 4\right)} \Longrightarrow - \frac{N}{\sqrt{|p(x)|}}\exp{\left(\frac 1 \hbar \int_{a}^{x} |p(x)| dx \right)}   $$

and:

$$ \frac{N'}{\sqrt{|p(x)|}} \cos{\left(\frac 1 \hbar \int_{x}^{a} |p(x)| dx - \frac \pi 4\right)} \Longleftarrow  \frac{N'}{2\sqrt{|p(x)|}}\exp{\left(-\frac 1 \hbar \int_{a}^{x} |p(x)| dx \right)}  $$

The WKB wavefunction at the classical turning point away from it is approximated by oscillatory sine or cosine function in the classically allowed region, represented in the left and growing or decaying exponentials in the forbidden region, represented in the right. The implication follows due to the dominance of growing exponential compared to decaying exponential. Thus, the solutions of oscillating or exponential part of wavefunctions can imply the form of wavefunction on the other region of potential as well as at the associated turning point.

Probability density
One can then compute the probability density associated to the approximate wave function. The probability that the quantum particle will be found in the classically forbidden region is small. In the classically allowed region, meanwhile, the probability the quantum particle will be found in a given interval is approximately the fraction of time the classical particle spends in that interval over one period of motion. Since the classical particle's velocity goes to zero at the turning points, it spends more time near the turning points than in other classically allowed regions. This observation accounts for the peak in the wave function (and its probability density) near the turning points.

Applications of the WKB method to Schrödinger equations with a large variety of potentials and comparison with perturbation methods and path integrals are treated in Müller-Kirsten.

Examples in quantum mechanics
Although WKB potential only applies to smoothly varying potentials, in the examples where rigid walls produce infinities for potential, the WKB approximation can still be used to approximate wavefunctions in regions of smoothly varying potentials. Since the rigid walls have highly discontinuous potential, the connection condition cannot be used at these points and the results obtained can also differ from that of the above treatment.

Bound states for 1 rigid wall
The potential of such systems can be given in the form:

$$V(x) = \begin{cases} V(x) & \text{if } x \geq x_1\\ \infty & \text{if } x < x_1 \\ \end{cases}$$

where $x_1 < x_2 $.

Finding wavefunction in bound region, ie. within classical turning points $x_1 $ and $x_2 $, by considering approximations far from $x_1 $  and $x_2 $  respectively we have two solutions:

$$\Psi_{\text{WKB}}(x) = \frac{A}{\sqrt{|p(x)|}}\sin{\left(\frac 1 \hbar \int_{x}^{x_1} |p(x)| dx +\alpha \right)}  $$

$$\Psi_{\text{WKB}}(x) = \frac{B}{\sqrt{|p(x)|}}\cos{\left(\frac 1 \hbar \int_{x}^{x_2} |p(x)| dx +\beta \right)}    $$

Since wavefunction must vanish near $x_1 $, we conclude $\alpha = 0 $. For airy functions near $x_2 $, we require $\beta = - \frac \pi 4   $. We require that angles within these functions have a phase difference $$\pi(n+1/2)$$ where the $$\frac \pi 2$$ phase difference accounts for changing sine to cosine and $$n \pi$$ allowing $$B= (-1)^n A $$.

$$\frac 1 \hbar \int_{x_1}^{x_2} |p(x)| dx = \pi \left(n + \frac 3 4\right) $$Where n is a non-negative integer. Note that the right hand side of this would instead be $$\pi(n-1/4)$$ if n was only allowed to non-zero natural numbers.

Thus we conclude that, for $n = 1,2,3,\cdots     $ $$\int_{x_1}^{x_2} \sqrt{2m \left( E-V(x)\right)}\,dx = \left(n-\frac 1 4\right)\pi \hbar $$In 3 dimensions with spherically symmetry, the same condition holds where the position x is replaced by radial distance r, due to its similarity with this problem.

Bound states within 2 rigid wall
The potential of such systems can be given in the form:

$$V(x) = \begin{cases} \infty & \text{if } x > x_2 \\ V(x) & \text{if } x_2 \geq x \geq x_1\\ \infty & \text{if } x < x_1 \\ \end{cases} $$

where $x_1 < x_2 $.

For $E \geq V(x)         $  between $x_1 $  and $x_2 $  which are thus the classical turning points, by considering approximations far from $x_1 $  and $x_2 $  respectively we have two solutions:

$$\Psi_{\text{WKB}}(x) = \frac{A}{\sqrt{|p(x)|}}\sin{\left(\frac 1 \hbar \int_{x}^{x_1} |p(x)| dx \right)}   $$

$$\Psi_{\text{WKB}}(x) = \frac{B}{\sqrt{|p(x)|}}\sin{\left(\frac 1 \hbar \int_{x}^{x_2} |p(x)| dx \right)}    $$

Since wavefunctions must vanish at $x_1 $ and $x_2 $. Here, the phase difference only needs to account for $$n \pi$$ which allows $$B= (-1)^n A $$. Hence the condition becomes:

$$\int_{x_1}^{x_2} \sqrt{2m \left( E-V(x)\right)}\,dx = n\pi \hbar $$where $n = 1,2,3,\cdots      $  but not equal to zero since it makes the wavefunction zero everywhere.

Quantum bouncing ball
Consider the following potential a bouncing ball is subjected to:

$$V(x) = \begin{cases} mgx & \text{if } x \geq 0\\ \infty & \text{if } x < 0 \\ \end{cases}$$

The wavefunction solutions of the above can be solved using the WKB method by considering only odd parity solutions of the alternative potential $$V(x) = mg|x|$$. The classical turning points are identified $x_1 = - {E \over mg}  $  and $x_2 = {E \over mg}    $. Thus applying the quantization condition obtained in WKB:

$$\int_{x_1}^{x_2} \sqrt{2m \left( E-V(x)\right)}\,dx = (n_{\text{odd}}+1/2)\pi \hbar$$

Letting $n_{\text{odd}}=2n-1 $ where $n = 1,2,3,\cdots      $, solving for $E $  with given $$V(x) = mg|x|$$, we get the quantum mechanical energy of a bouncing ball:

$$E = {\left(3\left(n-\frac 1 4\right)\pi\right)^{\frac 2 3} \over 2}(mg^2\hbar^2)^{\frac 1 3}. $$

This result is also consistent with the use of equation from bound state of one rigid wall without needing to consider an alternative potential.

Quantum Tunneling
The potential of such systems can be given in the form:

$$V(x) = \begin{cases} 0 & \text{if } x < x_1 \\ V(x) & \text{if } x_2 \geq x \geq x_1\\ 0 & \text{if } x > x_2 \\ \end{cases} $$

where $x_1 < x_2 $.

It's solutions for an incident wave is given:

$$V(x) = \begin{cases} A \exp({ i p_0 x \over \hbar} ) + B \exp({- i p_0 x \over \hbar}) & \text{if } x < x_1 \\ \frac{C}{\sqrt{|p(x)|}}\exp{(-\frac 1 \hbar \int_{x_1}^{x} |p(x)| dx )} & \text{if } x_2 \geq x \geq x_1\\ D \exp({ i p_0 x \over \hbar} ) & \text{if } x > x_2 \\

\end{cases} $$

Where the wavefunction in the classically forbidden region is the WKB approximation but neglecting the growing exponential, which is a fair assumption for wide potential barriers through which the wavefunction is not expected to grow to high magnitudes.

By the requirement of continuity of wavefunction and its derivatives, the following relation can be shown:$$\frac {|E|^2} {|A|^2} = \frac{4}{(1+{a_1^2}/{p_0^2} )} \frac{a_1}{a_2}\exp\left(-\frac 2 \hbar \int_{x_1}^{x_2} |p(x')| dx'\right)   $$

where $$a_1 = |p(x_1)|$$ and $$a_2 = |p(x_2)|   $$.

Using $\mathbf J(\mathbf x,t) = \frac{i\hbar}{2m}(\psi^* \nabla\psi-\psi\nabla\psi^*) $ we express the values without signs as:

$J_{\text{inc.}} = \frac{\hbar}{2m}(\frac{2p_0}{\hbar}|A|^2) $

$J_{\text{ref.}} = \frac{\hbar}{2m}(\frac{2p_0}{\hbar}|B|^2) $

$J_{\text{trans.}} = \frac{\hbar}{2m}(\frac{2p_0}{\hbar}|E|^2) $

Thus, the transmission coefficient is found to be:

$$T = \frac {|E|^2} {|A|^2} = \frac{4}{(1+{a_1^2}/{p_0^2} )} \frac{a_1}{a_2}\exp\left(-\frac 2 \hbar \int_{x_1}^{x_2} |p(x')| dx'\right)   $$

where $p(x) = \sqrt {2m( E - V(x))}       $, $$a_1 = |p(x_1)|$$ and $$a_2 = |p(x_2)|    $$. The result can be stated as $T \sim ~ e^{-2\gamma} $ where $\gamma = \int_{x_1}^{x_2} |p(x')| dx' $.

title: WKB approximation