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Blended Learning in K-12/Types of Blended Learning/multimedia virtual internet

This section focuses on blended learning in the classroom with the use of multimedia and internet resources. This includes the use of videos, virtual field trips, interactive websites, software packages, and broadcasting.

Blended learning often requires a reliance on technology use in the classroom. Because there is often a lack of access to technology outside of school, blending learning for many students, must occur in the classroom. The use of the internet for blending learning is wonderful. However, if students do not have access outside of the school day, the blended learning must occur in the classroom. The National Center for Education Statistics (NCES) compiled information from the U.S. Department of Commerce, Census Bureau, Current Population Survey, October 2003. The NCES put together the results in “Trends in the Well-Being of American Youth." These results provided the following information concerning computer usage; 62.6% of people ages 3-14 have home access, 72.2% of people ages 15-19 have home access, and 59.6% of people ages 20-24 have home access. Because access in no age group is 100%, teachers can not reasonably expect students to access required work outside the class period without arrangements being made in advance for access.  Because of this possible lack of access for students it is very important to accomplish blended learning in the class period by using videos or DVD's, virtual field trips, interactive websites, and broadcasting.

Video/DVD
Blended learning can include technology as common place today as using a video/DVD clip, segment, or movie. What is a video? According to the Corporation for Public Broadcasting (2002) the characteristics of video media are as follows
 * Video is the medium that you…are most familiar with.
 * Video can be distributed as “hard copy” on videocassette or DVD, digitized and delivered on the Web or CD, or distributed through specialized educational channels.
 * Video is especially good at telling a story or showing things that require narrative structure or moving images.
 * Video often has an emotional impact. It’s great at “taking you there and making you care.”
 * Today, VCRs (or DVD players) are widely accessible in classrooms and informal educational settings.

Most commonly, teachers think of buying videos to aid in enhancing the knowledge of the students for a particular topic. What many do not consider is that videos can be created by presenters, administrators, teachers, or classes and can serve many other purposes.

“Video can breathe meaning and life into nearly any lesson” (KQED 2005). According to a site by KQED public broadcasting, videos:
 * Provide a common experience for all students.
 * Generate Interest and stimulate imagination.
 * Offer a different perspective on or another approach to a topic.
 * Connect students with faraway places.
 * Demonstrate abstract ideas.
 * Stimulate the development of critical thinking skills.
 * Equalize educational opportunities.
 * Enhance self-respect and break down social stereotypes.
 * Promote critical viewing skills and media awareness.

Videos used in classroom settings, regardless who produced them, can be educational, promotional, training, event, and evaluative.

“Educational video is any video programming that contributes to the teaching/learning environment” (Lamb, Johnson 2002). The videos that are used to contribute to the classroom environment can cover any subject matter ranging from science to religion to business. These videos traditionally are the most common and they serve to introduce new topics or to reinforce previously learned topics.

Promotional videos are often used for companies trying to explain themselves or their products (Hotwire Media n.d.). These types of videos are not limited to the corporate world; they can have classroom uses as well. Teachers often are promoters of their product be it subject matter or classroom management. Using a self made or purchased promotional video can help explain teachers, the classroom, and the subject matter to the consumers of the products. Students.

Training videos are “Often targeted at a more specific audience than an educational film, and for use within a particular environment, video based training can add interest to any topic or process…” (Hotwire Media n.d.). Again, this type of video may be used more often in the corporate world, but they also can serve a purpose in a classroom. There are many processes that are taught and interest could be gained with a training video. The process of check writing is complicated for some, see the process unfold in a video could increase the knowledge and interest of the process. This would save instructional time and provide more time for the teacher to work one-on-one with students needing further instruction.

Events videos allow for a …”permanent audio-visual record of the event… (and allows teachers to) present the event to those not in attendance, or be used as a basis for discussion and evaluation” (Hotwire Media n.d.). Students giving presentations in class, or a guest speaker, would be examples of events in the classroom. This type of video would be student or teacher created. Absent students could view the events and not have lost any information from the day.

Evaluation videos and events videos can go hand in hand. Once the event video has been made of the class presentations, students and the teacher can refer back to the event video to evaluate the presentations. This can be a wonderful tool for teachers, allowing them to focus and really pay attention to the presenters, not grading the presentation as it goes. It can also be a wonderful for students, allowing them to look back at the event video and evaluate their own presentations.

Virtual Field Trips
Blended learning "Virtual Field Trips can be used in any number of ways to serve a variety of educational goals" (Tramline 2003). Fieldtrips have been a method of blending the learning and teaching methods of a class for a many years. The reality of funding shortages force schools to remain on campus. Using blended learning through the virtual fieldtrip is a wonderful opportunity. The virtual fieldtrip experience is an excellent model of a teaching strategy that was not possible before the advent of computers in the (school) classroom (Beal & Mason 1999). Going on a field trip has usually meant taking students out of the school building for some purpose. Today, due to budget restraints and other issues, it is becoming more and more difficult to take students out of the classroom to see things first hand. Schools with computer and internet access have the opportunity to go on fieldtrips with out spending any additional money or ever leaving the school building. “Virtual fieldtrips benefit students, families, schools, teachers, and communities” (Beal & Mason 1999). Virtual fieldtrips can take students to places they have personally visited, will be personally visiting. Once the virtual fieldtrip has been posted to the web, it is available to all people, any time, day or night (Tramline 2003). Virtual fieldtrips of all kinds are available, post-fieldtrip activity, pre-fieldtrip activity, fieldtrips made by others (not the teacher), and fieldtrips created by the teacher (Beal & Mason 1999).

The post-fieldtrip activity, as discussed by Beal and Mason (1999), blends student work, technologies, and locations involving student activities before, during, and after the fieldtrip. Before leaving for the “in person” field trip, assign each student or group with a particular task or subject matter area. Before and or during the trip, each person is responsible for gathering information of their assigned area. While on the fieldtrip, they are to gather information as well as pictures. Upon returning to the classroom, students are to compile their information and pictures into a presentation multimedia, which one depends on what is available to the students. Once each student or group has created their portion of the fieldtrip, the parts should be combined so that all students can view the virtual field trip and gain the same information. This field trip could then be used by other virtual visitors in the future if it is posted on the web.

Second is the fieldtrip category that addresses the blended learning virtual aspect (Beal & Mason 1999). With this pre-fieldtrip activity, the students go on a virtual fieldtrip created by someone else (partially the third category) before they leave their school building. Seeing the sites prior to their own arrival will give students insight and knowledge that might be missed during their visit. A pre-fieldtrip virtual fieldtrip can also give students a greater appreciation for what they will be seeing upon their arrival.

The third blended learning virtual fieldtrip requires the students to never leave the building and to use the computer and internet. The students "go" on the fieldtrip made by others and are able to gather information from places they can not visit in person as a class (Beal & Mason 1999). With the ability to go on a virtual fieldtrip, the places students can go are nearly endless. There are free virtual fieldtrips that can take students to every continent on earth. The locations range from a trip to a zoo, government agency, foreign museums, and national monuments and parks, just to name a few. The preparation on the teachers part is much less cumbersome than the preparation necessary to take students out of the school building and often the students learn just as much if not more in the computer lab.

Fourth, is the virtual fieldtrip with the blended learning created by the classroom teacher (Beal & Mason 1999). Teachers often take advantage of opportunities in the summer to go to conferences or seminars where trips are included or just parts of their own vacations. Teachers can put together the newly acquired information with pictures and create a virtual fieldtrip for their students for a much easier process and lesser cost than taking all the students out of the school building.

Interactive Websites
Blended learning oftentimes includes the use of interactive websites. The use of interactive web sites requires computer and internet access in the school. These sites provide another opportunity for teachers to use technology in their classroom, thus promoting blended learning. Interactive websites can be utilized within the class for those students who do not have internet access and can give other students the opportunity to expand knowledge if access is available privately. For these purposes, when we use the web, we are referring to the Internet. According to Dictionary.com WordNet 2.0 fro Princeton University, interactive is defined as “capable of acting on or influencing each other” (20032). When we put these two descriptions together we come to the conclusion that web/interactive is when people are capable of acting on or influencing the web. The Corporation for Public Broadcasting Web/Interactive (2002) provides three characteristics of web/interactive media.
 * They are not time-restricted and are not subject to a broadcast schedule.
 * They are visual, textual, and interactive.
 * They are nonlinear.

Blended learning web/interactive sites have elements within in them that allow people to act on or influence particular items on a particular page. The different elements allow influencing in different ways. The Corporation for Public Broadcasting Web/Interactive Media Elements (2002) addresses ten different web/interactive media elements. These ten elements are
 * Animated Narratives-reveal information progressively or along a user-determined path.
 * Audio and Video-voice and pictures (still or moving)
 * Discussion Environments-being able to share submissions with the larger audience.
 * Games-fun, and there may be a way to “win,” even though an educational agenda may be lurking within.
 * Illustrated Essays-“standard” Web pages of HTML text and graphics, least expensive type of Web page to produce.
 * Interactive Images-graphic features let users roll their cursor over or click on an image to provide greater text or graphic detail.
 * Interactive Simulations-computer-assisted explorations allow users to simulate real-world situations.
 * Interactive Timelines-present historical information in the context of other events of the period, organize events thematically, and allow users to read synopses and view images of people or artifacts.
 * Polls and Provocations-engage users in a controversy, requiring them to consider both sides of arguments before registering their opinion.
 * Resource Banks-annotated collections let users browse or search through carefully selected topical resources.

Software Packages
Blended learning with multimedia enhances both the teaching and learning processes. Blended learning with multimedia can take the shape of software available at school. Thousands of educational software packages exist on the market ranging from early reading and math skills to specific high school textbook supplements. The following is a continually growing list and brief overview of various educational software packages available for general reference and use, as well as specifically for Elementary, Middle School, and High School age groups.

 * Accelerated Math is a self-paced math learning program that helps students practice and master math skills. Teachers can tailor Accelerated Math to each student’s individual ability.  Accelerated Math automatically scores all assignments and tests and give both students and teacher immediate feedback.

 * Accelerated Reader Program motivates students to read by tracking progress with book quizzes. Students improve their reading skills as they progress throughout the Accelerated Reader book lists.  Teachers can utilize the book assessments and progress reporting generated by Accelerated Reader to track student progress and make book recommendations.

 * Encyclopedia Britannica Ultimate Reference Suite provides research level knowledge source. New features include Daily Content which serves up fascinating historical snapshots for the knowledge junkie and Homework Helpdesk: powerful tools for students.

 * Microsoft Encarta provides an encyclopedia, dictionary, atlas, and other educational reference materials. Encarta tools for students bring the world into the classroom with engaging and reliable content.

 * Microsoft PowerPoint is used to create projects and presentations from elementary age levels through high school and beyond. Students quickly learn the unique aspects of PowerPoint and enjoy learning technology while creating a presentation project.

Broadcasting
What is Broadcasting? According to the Merriam-Webster Online Dictionary, the definition of broadcasting is to transmit or make public by means of radio or television; to make widely known; to scatter seed (Webster, 2005). For purposes of Blended Learning, we will expand the definition to include web transmissions as well as radio and television transmissions. Broadcasting as blended learning incorporates student run radio, television, and websites in an educational setting.

Student led broadcasts of school related information has become increasingly popular in many schools and districts. Student broadcasts create a student-centered school environment among all students while fostering student leadership, developing technical skills, and building self-confidence and self-concept in participating students. Student broadcasting productions is defined as a type of blended learning by actively engaging students in the broadcasting, scripting, production processes, and technical direction of the program. Students from elementary grades through high school journalism classes utilize video, audio, and/or text and learn writing, editing, and publishing techniques through the production of online stories and links to student related interests.

How does broadcasting fit into blended learning? In general... Specifically...
 * K-12 students learn through active participation in broadcasting production, scripting, performance, and technical directing.
 * The general student body becomes engaged in student run activities.
 * Classroom students take pride in their work highlighted on classroom websites.
 * Media and Communications students learn practical applications of technical and communication skills through the active production of broadcasts.
 * Journalism students learn to create, edit, and produce news stories.
 * Video Production students learn the technical direction necessary behind the scenes in student broadcasts.

Examples of Student Broadcasting in the K-12 setting:

 * Oak Park Elementary Student Council sponsors a student led closed circuit television broadcasting program called “Good Morning Oak Park”. Oak Park fourth graders broadcast mini news, morning announcements, and lead the Pledge of Allegiance to the school every morning.  "Good Morning Oak Park" originated in the spring of 2003 on W.O.A.K., a school radio station.  W.O.A.K. quickly caught on in popularity and became a closed circuit television station during the fall of 2003.

 * Video Productions vocational students and Broadcast Journalism students of Hoover High School in North Canton, Ohio produce programs for both cable television and the school web site. Television broadcasts are through the North Canton City Schools Channel 11, an educational cable television station established for student use and production.  Students work collaboratively to produce both sites.  Journalism students create the feature stories and Video Production students run the technical aspects of the program.

 * Media and communications students from Carmel High School in Carmel, Indiana broadcast a student run radio station called WHJE. WHJE began in 1963 with one to two hour broadcasts each day and is now broadcasting on the air and through the web twenty-four hours a day, seven days a week.  The station develops and fosters student growth through broadcasting experience, production managers, engineers, and technical support.

 * Carmel High School also creates a bi-weekly online newspaper featuring student activities, school events, and announcements.


text:
User:Alwyn~enwikibooks

I am too paranoid to release my name and too boring to write anything interesting about myself.

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

title: User:Alwyn~enwikibooks


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Blended Learning in K-12/Types of Blended Learning/Classroom Websites Course Management Systems

The use of classroom websites and Course Management Systems (CMS) aid in the process of creating a blended learning environment. An article written by Klaus Schmidt, The Web-Enhanced Classroom, discusses four components necessary for successfully enhancing a course via the internet. The four components include: Administration, Assessment, Content and Community (Schmidt, 2002). One way to implement these components into a web-enhanced course is to use a Course Management System (CMS). A CMS allows for the administration of a web-enhanced course through the various tools included with the software. For example, a teacher is able to distribute handouts, set assignment deadlines, collect assignments and give quizzes from one location. This frees up time for the teacher, as stated by Schmidt, “A well-developed administrative component allows a teacher to spend more time interacting creatively with students and addressing higher level thinking skills rather than on mundane activities.”  Enhanced communication between the teacher and students is another administrative benefit gained from using a CMS. A teacher is able to post announcements to the entire class or send an individual email. Instant feedback on assignments can be sent and grades can be accessed by the student at any hour of the day. In addition, grading policies and deadlines can be clearly communicated in a CMS. Communicating between teacher, student, and even parent, can also occur more frequently with the use of a CMS. A teacher can distribute material to the class ahead of time; uing a CMS means that “assignments and lecture notes can be posted in advance, and students can have continual access to them” (Zirke, 2003).

Although a variety of CMS exist, this section focuses on three CMS examples (Moodle, WebCT, Blackboard).

Moodle
According to the moodle Website, "Moodle is a course management system (CMS) - a free, Open Source software package designed using sound pedagogical principles, to help educators create effective online learning communities" (2005).

Blackboard
Teacher Vivian Evans, gives a personal account of Blackboard, stating that "Blackboard has got some good features...It supports synchronous chat and discussion threads in a way that is very clear. Site administration is another strength.  You can control who has access to your site.  You can also look back at what happened previously by clicking on a past date to see what was discussed" (Evans, 2005).


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Blended Learning in K-12/Types of Blended Learning/Synchronous Asychronous Discussions

As indicated in Chapter 1, Blended learning combines technology with face to face instruction. Synchronous and asynchronous discussions are both types of internet communication that can be utilized in blended learning to fulfill the technology requirement. Both synchronous and asynchronous discussions utilize the internet to provide forums for use by the classroom teacher to either give instructions, facilitate office hours or conversation among students that would normally take place in a classroom setting. Asynchronous and synchronous discussions can be teacher or student led and can be guided by a pre-set format or take place in a more open setting, just like a classroom discussion. Both synchronous and asynchronous discussions have advantages and disadvantages. Asynchronous discussions allow time for reflection by the learner. In addition the asynchronous format allows for the diversity of the learner. It provides some flexibility for the learner to respond at his individual 'peak time', when he/she is at his best. The asynchronous model also enables each learner time to adequately respond. There is no need to 'grab the mic.' Each student is provided the opportunity to reflect and post a reply as deemed appropriate. The opportunity for reflection before response and flexibility of communication can produce greater depth of learning than the synchronous environment alone.(Donaldson & Conrad,2002) Certain situations best lend themselves to synchronous communications.Such activities include group meetings or activities requiring group consensus or simultaneous response. Synchronous discussions are especially useful for brainstorming or replicating the face to face situation. Synchronous discussions tend to be more successful when utilized by small groups. While both synchronous and asynchronous discussions have advantages and disadvantages, their use together in a blended learning situation is critical to the development of the online learning community.The types of asynchronous and synchronous discussions evaluated in this section include the use of Yahoo Groups, TappedIn, Blogs, and Elluminate.

Yahoo Groups
The Yahoo website provides free access to Yahoo Groups. In Yahoo Groups, anyone can originate a group of friends, family or others with similar interests. In a blended learning situation, the teacher can create a group or assign groups within the class to utilize Yahoo as their 'meeting place'. Within the group, there are options for message posting, synchronous chats, links to other sites as well as a place to post photos, make a calendar and poll the group members. As a group, Yahoo provides great flexibility for sharing opinions and discussion both asynchronously and synchronously. The asynchronous format functions much like a message board with members of the group posting and responding to other posts. Messages are listed chronologically and easy to follow. Only members of the group are allowed to post and members are identified by their sign in name. The originator of the group becomes the moderator and as such can use different options to insure the continuity of messages and the appearance of the asynchronous site. Messages posted on the site can also be emailed to members of the group. The Yahoo site makes it easy to communicate with members of a specific group. It is basically like using email. You simply click on post and type your message. It appears on the message site for members of the group to see.The subject of the message appears at the top of the message in a larger font and different color. The sender's name and other information appears to the right of the message body. It is a very easy format to follow for asynchronous discussions. The synchronous function of Yahoo Groups is found in the Chat section. It is similarly easy to access by clicking on Chat in the menu after signing in to your group. Once at the chat site, you can type your message into the dialogue box, hit send and it is immediately posted. Others can then respond to the dialogue. This format is a more expedient way to carry on a discussion although it can seem disjointed and does not always flow smoothly. One needs to establish a topic and some ground rules so everyone is not talking at once. It works very much like instant messaging except everyone is messaging simultaneously.There are a few options for the participants to choose if they are away from the computer.

TappedIn
TappedIn is a web-based learning environment created by SRI International to transform teacher professional development. Tapped In enables teachers to implement effective, classroom centered learning activities through the use of online tools, resources, member colleagues, scheduled class events, and technical support. Tapped In provides teachers with online learning strategies, collaborative member support, and online continued professional development courses.

Tapped In went online in 1997 and has continued to grow and expand it's teacher network. Tapped In currently has ongoing funding from the National Science Foundation and from Sun Microsystems. Tapped In is currently a free service to teacher members.

Teachers can use Tapped In to manage online courses, create teacher chat rooms, and conduct office hours. Organizations registered with Tapped In receives a Tapped In virtual building with three floors. The ground floor contains member logins, help desk, and public rooms. The second floor contains group rooms deemed as public, moderated, or private. The third floor is reserved for personal member offices.

Tapped In offers after school teacher collaboration sessions called the After School Online (ASO) in various subject matters. A monthly schedule of ASO topics is contained on Tapped In's homepage and is emailed to every Tapped In member. A sample of monthly activities and discussions can be viewed on this monthly calendar.

Tapped In can be used both synchronously and asynchronously. Teachers can create and manage class groups with student accounts, set up course calendars, allow guest logons, send mailings, conduct online chats and private messaging, create discussion boards, and store files and URLs. Courses can utilize synchronous chats through office hours and class chat sessions; and asynchronous discussions through message boards. Tapped In automatically logs discussion transcripts and emails the transcript to group participants. Students who are not present for a chat can later view the discussion text through Tapped In.

Blogs
Blog is a term coined for the combination of two words, web and log. As part of a blended learning project,it is an asynchronous form of online discussion. A blog is a publicly accessible website which contains a journal or diary of sorts. Anyone can initiate a blog either as a part of another website or personal web page or a blog can stand alone. The author of the blog can choose to write in this journal as she pleases with no filters or censorship. Blogs span a wide variety of topics. Some blogs are followed by a huge readership where others may suffice only for a family or small close knit group. According to Michael Berkman in his Blog Guide Book (Sept.2005)there are reportedly over 11 million blogs on the web. Blogs offer a forum for many people to state their opinions or comment on other's opinions. Blogs seem to offer a more fluid discussion than other group chats or asynchronous types of forums. Because blogs are in the public domain, a topic of intense interest or current event may be accessed continually with one or more threads flowing throughout the blog. This is different than an asynchronous discussion in which the reader is directed to comment on a specific topic or question. It is similar to a face to face discussion in the rapidity in which responses can appear and the opinionated nature of the comments and responses. In a blended learning situation, blogs can be used as a discussion forum for students or as a reference source for parents. Blogs can also be used as a publishing site for student work, with appropriate security and permission issues addressed, of course. Teachers need to proceed with caution when using blogs as students may tend to read blogs as resource sites and not properly evaluate the information gained from the blog sites. Blogs could provide a great medium to enhance student writing through the use of technology. Elementary grade students are frequently encouraged to use journal writing as story starters so it would be a logical jump to move that journal writing to a blog site. Additionally blogs could be used toward improving literacy skills as students read and peer edit other student's blogs. The Daily Oral Language activity is another possible blog use. Blogs offer the most flexibility for use as an asynchronous forum. There are numerous free guides and sites to set up blogs.

Eluminate
Eluminate is a synchronous forum used for online discussions. It is widely used in both the academic arena as well as the corporate world. As a teaching tool, it provides an online source similar to a chat room for invited guests to meet and replicate a face to face classroom situation.At the Eluminate site, a moderator can conduct the discussions by stating a specific topic or listing it on the accompanying whiteboard. The moderator has several options to allow varying degrees of participation by the students. Eluminate provides moderators with the ability to use online quizzes and polls. A whiteboard is also available to repeat or illustrate with text or graphics. Whiteboard access for students is controlled by the moderator. In addition the moderator can present websites or related information on the whiteboard. The whiteboard can also serve to demonstrate power point presentations. Participants may discuss either by using a microphone for live voice or typing responses in the text box. Eluminate provides options for participants to raise their hand before speaking, to applaud and includes a system of tallies for polling. Although conversations seem to flow rapidly in the text box, there is often incontinuity as participants post comments frequently changing the subject. It can also be distracting as the text conversation continues while someone is talking. This actually seems to be somewhat rude. One of the advantages of using Eluminate is the fact that it is extremely user friendly. It is relatively simple to acknowledge the invitation, access the site and join the discussion. Although a tutorial is available students can learn to navigate the site quite easily as a part of the first lesson. Sound quality is quite good and accessing the audio component is not difficult. One of the disadvantages of the Eluminate program is the cost factor. The academic version of Eluminate ranges in price from $2400 for a one year three seat team edition to $7000. for a 10 seat team edition. This cost is no doubt prohibitive for some schools especially elementary districts. Currently Eluminate is used most often by higher education institutions. Although it has some valid use for elementary level districts, the cost is no doubt prohibitive. As a teaching tool, Eluminate serves to replicate the face to face discussion one might have in a classroom. It lends itself most easily to the higher grade levels for a few reasons. Although Eluminate is easy to use, it requires higher level typing skills to keep up with the conversation. It is also necessary to access the talk button to use the audio portion of the forum and to adjust the volume of speaker and mic as necessary. This would be a difficult skill for an elementary aged student although I think it would be possible to involve junior high aged students. Eluminate could certainly be a resource for secondary schools and something students would enjoy using. Utilizing the synchronous discussion strictly for lecturing becomes stale. To fully realize the potential, the instructor should access the whiteboard either for illustrations or for a power point presentation. Eluminate offers many options for the instructor to integrate technology into the classroom in a meaningful way.

After using Tapped In, Blogs, and Elluminate I would have to say that Elluminate is by far the best product. I love the aspect you can present PowerPoint’s, chat by typing, watch streaming videos and communicate to others in the class. Before reading this article, I was wondering why Elluminate was not used more. I did not realize the cost was so high! I can’t help but wonder if the price came down if more people would use this product. - Dale Donner


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Talk:Blended Learning in K-12/Types of Blended Learning

I just made a bunch of changes to the format of our chapter and forgot to long in, sorry. These are changes as suggested in the office hours 10/04. Cathy

The number sequence that identifies the changes I made is 12.216.211.73 sorry again. Cathy

I thought I was logged in since my name appears on the top as logged in on some pages. Apparently not all. I made the major changes today to the main chaper intro page. I was listed as 12.217.211.73. Sorry. Again. Cathy

I was not 217 it was 216 (area cod is 217) Cathy


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Quantum Mechanics/The Hydrogen Atom

Introduction
By now you're probably familiar with the Bohr model of the atom, which was a great help in classifying the position of fundamental atomic specta lines. However, Bohr lucked out in more ways than one. The hydrogen atom turns out to be one of the few systems in Quantum Mechanics that we are able to solve almost precisely. This has made it tremendously useful as a model for other Quantum Mechanical systems, and as a model for the behavior of atoms themselves.

Fundamentals
We can assume that the hydrogen atom is governed by the Coulomb potential, namely:

$$ V(r) = -\frac{e^2}{4 \pi \epsilon _0} \frac{1}{r} $$

such that, $$ H\Psi = -\frac{\hbar ^2}{2m}\frac{d^2\Psi}{dx^2} - \frac{e^2}{4 \pi \epsilon _0} \frac{1}{r} $$

Obviously, simply by inspection, we can see that the Hydrogen Atom is a spherical system. Hence it makes more sense to deal with the Hydrogen atom in spherical coordinates. One should remember at this point that, via Separation of variables, you can obtain the solution to the spherical Laplacian in three-dimensional space:

$$ \nabla ^2f = {1 \over r^2} {\partial \over \partial r} \left( r^2 {\partial f \over \partial r} \right) + {1 \over r^2 \sin \theta} {\partial \over \partial \theta} \left( \sin \theta {\partial f \over \partial \theta} \right) + {1 \over r^2 \sin^2 \theta} {\partial^2 f \over \partial \phi^2} $$

the solutions to this function when we use separation of variables inside a Hamiltonian gives us two different functions, the Radial Wave functions (not useful now, but good to know):

$$ A \cdot J_l \left(Z_{nl}\frac{r}{a} \right) $$

where $$J_l$$ are the spherical Bessel functions of type l, and $$Z_{nl}$$ are the zeroes of said Bessel functions.

The other component, the angular component are the Spherical harmonics which are explored in detail on Wikipedia.

Calculations
Essentially, we're ahead of the game at this point. We already know the answers. The hydrogen wave function will have to involve the spherical solutions to the Laplacian and will be related to both the angular and radial components. This is most fortunate; for us to attempt to solve the Laplacian while doing the hydrogen atom would be difficult. However, we have some tasks left. The situation must be normalized, and we must deal with the fact that our potential has a pesky r dependence.

Results
We end up with the results that you knew we were going to. We can write down the hydrogen wave equation as:

$$ \Psi _{nlm}(r, \phi, \theta) = R_{nl}(r)Y^l_m(\theta, \phi) $$

where $$Y^l_m(\theta, \phi)$$ are the spherical harmonics.

title: Quantum Mechanics/The Hydrogen Atom


text:
Talk:Quantum Mechanics/The Hydrogen Atom

Hopefully I'll be back to fill some of this in later. I suspect we should leave the derivation of the solutions to the spherical laplacian to our mathematical colleagues.

Alwyn 02:43, 5 October 2005 (UTC)


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Forth/Manipulating the Stack

The Parameter Stack

A data structure common to many languages is the stack. A LIFO (last-in first-out) type of stack called the parameter stack (to distinguish it from the return stack) is frequently the implied source and destination for many of the data and arithmetic operations performed in FORTH.

Typical operations will find their input parameters on the stack, usually remove (pop) these inputs, and then place the new results back onto the stack (push).

While FORTH has variables, arrays, strings, and other data structures, the use of the stack is combined with the philosophy of the language to achieve a variety of advantages.

 * If a piece of code only uses the stack for its inputs, outputs, and intermediate values, it is inherently re-entrant in almost every case.
 * If a piece of code maintains stack parity, that is, neither removes or abandons values on the stack between its beginning and end, then a call to it can be inserted anywhere in a body of code.
 * The stack is like a switchyard that can get data to and from anywhere. Data can be switched between all parts of the system by reading it or writing it to the top element of the stack.
 * Op codes do not need to use bits to specify register values, instead, two RISC machine style instructions are used in sequence, analagous to LOAD then ADD. These simpler instructions allow efficient implementation.

When you type a number, it goes on the stack. When you type several numbers, they all go on the stack, with the most-recent number on the top of the stack. For example, immediately after typing 7 22 -8 14 9 and hitting ENTER, the stack appears like this:

cell #  contents 0        9        (TOS) 1       14        (NOS) 2       -8                3        22               4         7

Many programmers document a word using a stack diagram, with two "pictures" of the stack (with the TOS furthest to the right), before and after the word executes.

SWAP ( ... a b -- ... b a )

DROP ( ... x y z -- ... x y )

DUP ( ... x y z -- ... x y z z )

ROT ( ... a b c d -- ... a c d b )

title: Forth/Manipulating the Stack


text:
User talk:Crystal Matrix~enwikibooks

If you cast a wikiversity vote, please make a link at your Wikimedia meta-wiki user page linking back to your wikibooks user page. If you do not do so, your vote will not count. --JWSurf 02:59, 5 October 2005 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Crystal Matrix. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Crystal Matrix~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:06, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 04:49, 19 April 2015 (UTC)

title: User talk:Crystal Matrix~enwikibooks