text:
Aristotle/On the Soul: Outline

This is a short outline of "Peri Psyche", an attempt to provide one summary sentence for each paragraph in the Lawson-Tancred translation.

Key: B1C1p1 means Book 1, Chapter 1, paragraph 1.

Note: the word "psyche" (ψυχή) is left untranslated so as to let the reader attempt to discover what Aristotle meant by the word.

Chapter 1
B1C1p1: Aristotle was thinking of “psyche” as a fundamental principle of living things and an important part of the natural world.

B1C1p2: Aristotle points out the fact that it is not clear how best to try to understand the fundamental principles of living things.

B1C1p3: Aristotle notes that while many people try to understand the fundamental principles of living things by thinking about people, we should not ignore the fact that there are many types of living organisms and we can explore which types of organisms share the various human abilities such as perception and thinking.

Chapter 2
B1C2p4: Aristotle asks if “psyche” is something that only exists as a feature of a living organism or is it something that can exist independent of a particular body and concludes that we have no way of studying “psyche” outside of the context of the actual physical bodies of living things. B1C2p1: Aristotle identifies self-generated movement and perception as two key aspects of “psyche” and reviews some previously published ideas about how “elements” such as fire might make it possible for living things to produce movement.

B1C2p2: Aristotle mentions past discussions by people such as Anaxagoras about the idea that mind or “psyche” might be the source of self-generated movement produced by living things.

B1C2p3: Aristotle reviews the Platonic theory that perception and knowing have a fundamental geometrical basis in that the “elements” are formed from numbers and the elements combine to make perception, knowledge and mind.

B1C2p4: Aristotle moves from the specific suggestion that the “psyche” is in some fundamental way reducible to numbers to a general discussion comparing 1) the idea that the “psyche” is non-physical to 2) the alternative that if it is physical then it must be composed of the most disembodied of the “elements”: fire.

B1C2p5: Aristotle mentions the theories of several people including Democritus who had tried to account for “psyche” in terms of special components such as a type of atom that is “productive of motion” or one of the “elements” such as air or water.

B1C2p6: Summarizing the views of others, Aristotle concludes that many commentators have associated “psyche” with the self-generation of movement, perception, cognition and the idea of an existence beyond the physical.

Chapter 3
B1C3p1: Having outlined the ideas of others, Aristotle begins his analysis by asking if generation of movement is something that is fundamentally associated with “psyche”, or if movement might just be something that we mistakenly attribute to “psyche”.

B1C3p2: Aristotle starts by noting that anything intimately involved with movement must exist in space and be subject to some force that controls the movement.

B1C3p3: Aristotle suggests that if the “psyche” is the source of movement of the bodies of living things then we should wonder if the “psyche” itself can move, say out of and then back into a dead body.

B1C3p4: Aristotle asks if “psyche” produces the motion of living things by means of thought and the making of choices or if “psyche” is itself moved in response to perceptions.

B1C3p5: Aristotle explores the theory of mind and motion from the Timaeus, raising several objections to Plato’s analogy between the movement of heavenly bodies and the production of movement and thought in living things.

B1C3p6: Aristotle concludes that all dualistic theories that attribute self-generated motion of the bodies of living things to the motion of the “psyche” are not adequate because they explain nothing about how the “psyche” interacts with the body nor how motion of the “psyche” is transferred to motion of a body.

Chapter 4
B1C4p1. Introduction to the theory that “psyche” is in some way explained as a mixture of components that produce a balanced system.

B1C4p2. Aristotle suggests that a theory of balance is more suited to health than to supposed functions of “psyche” such as the production of movement.

B1C4p3. Aristotle also expresses doubt that perception and thought can be produced by some correctly adjusted balance of component parts.

B1C4p4. Aristotle wonders if it is the case that is “psyche” is a correct ratio of components, that what prevents that ratio from being produced multiple times in several different places in the same body.

B1C4p5. Rather than say that "psyche" moves, Aristotle suggests that perception might involve a movement of something towards the “psyche” and that memories might come from the “psyche” and help drive motion in the body.

B1C4p6. Aristotle discusses the idea that thought might be based on a fundamental dualism of an eternal part that is associated with a body (and possibly cannot be destroyed) and a second part that depends on the health of the body and can decline with age as the body (a vehicle for the "psyche") decays.

B1C4p7. Aristotle suggests that we do not need to assume that the “psyche” itself moves and he concludes in particular that it is silly to say that “psyche” is a self-moving number.

B1C4p8. Aristotle expresses doubt that some simple atom can account for motion and “psyche”, asking what would keep all bodies from containing these atoms and having “psyche”.

B1C4p9. Aristotle concludes that neither some sort of special atom or some special number can account for the self-generation of movement in living things, let alone perception and reasoning.

Chapter 5
B1C5p1. Aristotle turns to consideration of the idea that “psyche” must be composed of the elements because it requires something made from the elements in order to perceive objects made from the elements.

B1C5p2. Aristotle dismisses the idea that “psyche” allows us to perceive “like by like” because it would seem to require that that “psyche” come equipped not just with all of the elements but also copies of the patterns and formulae that describe exactly how the elements exist in all objects we can perceive.

B1C5p3. Aristotle wonders how it would be possible for a “psyche” composed of all things to avoid being a complex substance that would have to fit into a body.

B1C5p4. Aristotle wonders, if “psyche” is produced by a composite of the elements, then why do all things composed of elements not have “psyche”.

B1C5p5. Aristotle makes the point that various living things have different abilities (only some move, breath or perceive) and wonders then how if being composed of the elements can account for “psyche”, how it would also account for differences between living things.

B1C5p6. Aristotle dismisses the idea that “psyche” is in every part of the universe, suggesting that if it were, then it would have to be homogeneous and unable to account for the different behaviors of different living things.

B1C5p7. Aristotle says that “psyche” is the source of growth, perception, thought, belief, appetite and desire and wonders what would hold all of the parts of “psyche” together if “psyche” itself has parts.

B1C5p8. Aristotle again mentions the fact that the bodies of some plants and animals can be divided into parts, each of which continue to live, suggesting that “psyche” can not be associated with any particular part of the body.

B1C5p9. Aristotle repeats the idea that plants have a kind of “psyche” that does not include perception.

Chapter 1
B2C1p1. Aristotle introduces his own conceptualization of “psyche” as the fundamental organizing principle of potentially living things.

B2C1p2. As a general statement about all types of “psyche”, Aristotle suggests the formula that “psyche” is the fundamental organizing principle any body with organs.

B2C1p3. Aristotle insists that “psyche” is a substance that is distinct from matter; that which is needed in addition to the matter of a living body.

Chapter 2
B2C2p1. Aristotle starts to define the parts of “psyche” by saying that plants only have the nutritive part (including a capacity for self-generated motion of growth).

B2C2p2. Aristotle lists other parts of “psyche” that only certain living things have (perception, pain, appetite, imagination, desire and intellect) and raises the question of if some of these parts might exist independent of a body.

B2C2p3. Aristotle indicates that each type of body has its own appropriate “psyche” (a particular “psyche” can not exist in just any type of body, say by moving between different bodies).

Chapter 3
B2C3p1. Aristotle raises the question of if all animals have imagination.

B2C3p2: Aristotle raises the question of why it is that there seems to be an ordered series of abilities in living things from nutritive (in plants) to perception (in animals) starting with touch as the most common with other senses like vision in some animals and  imagination and reason the most rare.

Chapter 4
B2C4p1: Aristotle states his plan: to first examine each of the abilities associated with “psyche” (nutritive, perception, imagination and reason) and then identify the principle(s) general and common to them all.

B2C4p2: Aristotle notes that all living things obtain nutrients in order to reproduce.

B2C4p3: Aristotle identifies “psyche” as the cause of the behaviors of living things such the roots of plants growing down into the ground.

B2C4p4: Aristotle provides an outline of nourishment with reference to digestion of food and the production of heat.

Book Three
Your turn. Continue reading and add your summary comments here. This book turns more directly toward the question of man and the four different kinds of imagination.

title: Aristotle/On the Soul: Outline


text:
German grammar/Haben

In German, the word "haben" is the infinitive of "to have".

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

title: German grammar/Haben


text: User talk:Zakwhich

title: User talk:Zakwhich


text:
German Language/List of German verbs

This is a short list of German verbs useful for the beginner. They are listed in alphabetical order by infinitive. The past tense and past participle are listed after the infinitive, with the English equivalent in parenthesis. Where the stem changes in the present tense, the change is indicated in parenthesis following the infinitive.

a-c

 * abweisen, wies ab, abgewiesen (to reject)
 * aus gleichen, glich aus, ausgeglichen (to balance)
 * backen (bäckt), backte, gebacken (to bake)
 * befehlen (befiehlt), befahl, befohlen (to order, command)
 * beginnen, begann, begonnen (to begin)
 * beißen, biss, gebissen (to bite)
 * betrügen, betrog, betrogen (to cheat)
 * beweisen, bewies, bewiesen (to prove)
 * bewerben (bewirbt), bewarb, beworben (to apply)
 * biegen, bog, gebogen (to bend)
 * bieten, bot, geboten (to offer)
 * binden, band, gebunden (to tie)
 * bitten, bat, gebeten (to ask)
 * blasen (bläst), blies, geblasen (to blow)
 * bleiben, blieb, ist geblieben (to stay, remain)
 * braten (brät), briet, gebraten (to fry)
 * brechen (bricht), brach, gebrochen (to break)
 * brennen, brannte, gebrannt (to burn)
 * bringen, brachte, gebracht (to bring)

d-f

 * denken, dachte, gedacht (to think)
 * dringen, drang, ist gedrungen (to penetrate)
 * dürfen, darf, durfte, gedürft (to be allowed to)
 * eilen, eilte, geeilt (to hurry)
 * einladen (lädt ein), lud ein, eingeladen (to invite)
 * empfangen (empfängt), empfing, empfangen (to recieve)
 * empfehlen (empfiehlt), empfahl, empfohlen (to recommend)
 * entscheiden, entschied, entschieden (to decide)
 * erklingen, erklang, ist erklungen (to resound)
 * erscheinen, erschien, ist erschienen (to appear)
 * ertrinken, ertrank, ist ertrunken (to drown)
 * essen (isst), aß, gegessen (to eat)
 * fahren (fährt), fuhr, ist gefahren (to go by vehicle)
 * fallen (fällt), fiel, ist gefallen (to fall)
 * fangen (fängt), fing, gefangen (to catch)
 * finden, fand, gefunden (to find)
 * fliegen, flog, ist geflogen (to fly)
 * fliehen, floh, geflohen (to flee)
 * fressen (frisst), fraß, gefressen, (to eat (of animals))
 * frieren, fror, gefroren (to freeze)

g-k

 * geben (gibt), gab, gegeben (to give)
 * gehen, ging, ist gegangen (to go)
 * gelingen, gelang, ist gelungen (to succeed)
 * genießen, genoss, genossen, (to enjoy)
 * geraten (gerät), geriet, geraten (to get)
 * geschehen (geschieht), geschah, ist geschehen (to happen)
 * gewinnen, gewann, gewonnen (to win)
 * gießen, goss, gegossen (to water)
 * gleiten, glitt, ist geglitten (to slide)
 * greifen, griff, gegriffen (to reach)
 * haben (hat), hatte, gehabt (to have)
 * halten (hält), hielt, gehalten (to hold)
 * hängen, hing, gehangen (to hang)
 * heben, hob, gehoben (to raise)
 * heißen, hieß, geheißen (to be called)
 * helfen (hilft), half, geholfen (to help)
 * kaufen, kaufte, gekauft (to buy)
 * kennen, kannte, gekannt (to know)
 * kommen, kam, ist gekommen
 * können (kann), konnte, gekonnt (to be able to)
 * kriechen, kroch, ist gekrochen (to creep)

l-r

 * lassen (lässt), ließ, gelassen, (to let)
 * laufen(läuft), lief, ist gelaufen (to walk)
 * leiden, litt, gelitten (to suffer)
 * leihen, lieh, geliehen (to lend)
 * lesen (liest), las, gelesen (to read)
 * liegen, lag, gelegen (to lie down)
 * lügen, log, gelogen (to lie)
 * mahlen, mahlte, gemahlen (to grind)
 * messen (misst), maß, gemessen (to measure)
 * mögen (mag), mochte gemocht (to like)
 * (möchten is imperfect subjuctive (to want))

 * müssen (muss), musste, gemusst (to have to)
 * nehmen (nimmt), nahm, genommen (to take)
 * nennen, nannte, genannt (to name)
 * pfeifen, pfiff, gepfiffen (to whistle)
 * raten (rät), riet, geraten (to guess)
 * reiben, rieb, gerieben (to grate)
 * reißen, riss, gerissen (to tear)
 * reiten, ritt, ist geritten (to ride on horseback)
 * rennen, rannte, ist gerannt ( to run)
 * riechen, roch, gerochen (to smell)
 * rufen, rief, gerufen

s

 * saufen (säuft), soff, gesoffen (to drink (of animals))
 * scheinen, schien, geschienen (to shine)
 * schieben, schob, geschoben (to push)
 * schießen, schoss, geschossen (to shoot)
 * schlafen (schläft), schlief, geschlafen (to sleep)
 * schlagen (schlägt), schlug, geschlagen (to beat)
 * schleichen, schlich, ist geschlichen (to sneak)
 * schließen, schloss, geschlossen (to lock)
 * schneiden, schnitt, geschnitten (to cut)
 * schreiben, schrieb, geschrieben, (to write)
 * schreien, schrie, geschrien, (to shout)
 * schweigen, schwieg, geschwiegen (to keep quiet)
 * schwimmen, schwamm, ist geschwommen (to swim)
 * sehen (sieht), sah, gesehen (to see)
 * sein (ist), war, ist gewesen (to be)
 * singen, sang, gesungen (to sing)
 * sinken, sank, ist gesunken (to sink)
 * sitzen, saß, gesessen (to sit)
 * sprechen (spricht), sprach, gesprochen (to speak)
 * springen, sprang, ist gesprungen (to spring, jump)
 * stechen (sticht), stacht, gestochen (to poke)
 * stehen, stand, gestanden (to stand)
 * stehlen (stiehlt), stahl, gestohlen (to steal)
 * steigen, stieg, ist gestiegen (to climb)
 * sterben (stirbt), starb, ist gestorben (to die)
 * stoßen (stößt), stieß, gestoßen (to push)
 * streichen, strich, gestrichen (to stroke)

t-z

 * tragen (trägt), trog, getragen (to carry)
 * treiben, trieb, getrieben (to drift)
 * treten (tritt), trat, ist getreten (to step)
 * trinken, trank, getrunken (to drink)
 * tun, tat, getan (to do)
 * unterscheiden, unterschied, unterschieden (to distinguish)
 * verbergen (verbirgt), verbarg, verborgen (to hide)
 * verlieren, verlor, verloren (to lose)
 * verschwinden, verschwand, ist verschwunden (to disappear)
 * verweisen, verwies, verwiesen (to banish)
 * wachsen (wächst), wuchs, ist gewachsen (to grow)
 * wenden, wandte, gewandt (to turn)
 * werfen (wirft), warf, geworfen (to throw)
 * wiegen, wog, gewogen (to weigh)
 * wissen (weiß), wusste, gewusst (to know)
 * zerbersten (zerbirst), zerbarst, ist zerborsten (to burst)
 * ziehen, zog, gezogen (to pull, move)

title: German Language/List of German verbs


text:
Schrödinger equation

The Schrödinger equation is an equation that is fundamental to quantum theory. The time independent Schrödinger equation looks like

 * $$ \hat{H} \psi = E \psi .$$

The $$ \hat{H} $$ is called the Hamiltonian Hamiltonian mechanics. $$ \psi \,\; $$ denote the wavefunctions.

How to construct the Schrödinger equation for a system
The operator $$\hat{H}$$ is called the Hamiltonian. It contains two parts:

 * 1) The kinetic energy, denoted by the operator $$\hat{T}$$
 * 2) The potential energy, denoted by the operator $$\hat{U}$$

These two operators represent the principal types of energies in any physical system. Putting these two parts together, we can write this as $$\hat{H} = \hat{T} + \hat{U}$$. We can think of the Hamiltonian as a mathematical object that encodes how the energies in a system can be distributed.

Kinetic energy operator
In classical mechanics, we know that the kinetic energy of a moving particle is given by

 * $$E = \frac{1}{2} mv^2 = \frac{1}{2} m \vec{v} \cdot \vec{v}$$

in which $$m$$ corresponds to the mass of the particle, and $$\vec{v}$$ is its velocity. Noting that classically the linear momentum $$\vec{p}$$ is given by $$\vec{p} = m \vec{v}$$, so the kinetic energy can also be written as

 * $$E = \frac{p^2}{2m}$$.

In order to get the quantum mechanical version of this, we substitute all occurrences of the momentum $$\vec{p}$$ with

 * $$\vec{p} \to -i \hbar \nabla$$,

where $$\nabla$$ is the vector analogue of the partial differential operator $$\frac{\partial}{\partial x}$$.

Hence, the kinetic energy operator is given by

 * $$\hat{T} = - \frac{\hbar^2}{2m} \nabla^2 $$.

Total energy operator and the time dependent Schrödinger equation
The total energy operator introduces the time propagation to the wavefunctions so the time dependent Schrödinger equation tells how the quantum system developes is time while ist was found is some state at the original time. It is basically constructed from the condition that its operation on time dependent oscillatory factors characteristic to the plane waves obtained from the classical wave equation describing the mechanical waves like sound or the waves on the water surface should produce the energy quanta $$\hbar \omega$$ as the eigenvalues from the eigen-equation namely
 * $$\hat{E}_{TOT} e^{- i \omega t}= \hbar \omega e^{- i \omega t}$$

One therefore may readily guess it as
 * $$\hat{E}_{TOT} = i \hbar\frac{\partial}{\partial t} $$

While te total energy in the classical mechanics is normally equal to the Hamiltonian the time dependent Schrödinger equation is obtained by equalizing the two:

 * $$ \hat{H} \psi = i \hbar \dot \psi .$$

Example 1: The ground state of the hydrogen atom
The time independent Schrödinger equation for the electron in the Coulomb potential in the spherical coordinates takes the form:

 * $$ -\frac{\hbar^2}{2 m} \left [

{1 \over r^2} {\partial \over \partial r} \left(r^2 {\partial  \over \partial r} \right) + {1 \over r^2 \sin \theta} {\partial \over \partial \theta} \left(\sin \theta {\partial \over \partial \theta} \right) + {1 \over r^2 \sin^2 \theta} {\partial^2 \over \partial \varphi^2} \right ] \psi(r,\theta,\varphi) -\frac{e^2}{4 \pi \epsilon_0 r} \psi(r,\theta,\varphi)= E \psi(r,\theta,\varphi). $$ For the ground state which is the state with the lowest possible $$E$$ we seek the solution in the simplest possible form not dependent on the spherical angles $$\theta$$ and $$\varphi$$. The Schrödinger equation greatly simplifies to the second order ordinary partial differential equation of the one radial variable:
 * $$ -\frac{\hbar^2}{2 m} \left [

{1 \over r^2} {\partial \over \partial r} \left(r^2 {\partial  \over \partial r} \right) \right ] \psi_0(r) -\frac{e^2}{4 \pi \epsilon_0 r} \psi_0(r)= E_0 \psi_0(r). $$ The part of it contains derivatives multiplied by the various powers of the $$r$$ variable and we guess the solution in the exponential form since the exponential function is the eigenfunction of the differentiation operator while the derivative of the exponential function is proportional to it:
 * $$\psi_0(r)=N e^{-a r} $$

Substituting it to the Schrödinger equation we obtain the following equation:
 * $$-\frac{\hbar^2}{2 m} \left [ -\frac{2 a}{r} + a^2\right ]\psi_0(r)-\frac{e^2}{4 \pi \epsilon_0 r} \psi_0(r)=E_0 \psi_0(r)$$

The only way this equation is valid for all values of $$r$$ is that the coefficient multiplying the $$1/r$$ is equal to $$0$$:
 * $$\frac{a \hbar^2}{ m r} = \frac{e^2}{4 \pi \epsilon_0 r}$$

that gives the value of the Bohr radius $$a_0$$ (the range how the ground state mostly extents radially):
 * $$a_0=1/a=\frac{4 \pi \varepsilon_0 \hbar^2}{m e^2}$$

and the ground state energy
 * $$E_0=-\frac{a^2 \hbar^2}{2 m}=-\frac{m e^4}{8 {\varepsilon_0}^2 \pi^2 \hbar^2 }$$.

Example 2: Time dependent perturbation theory of weak field ionization
The first thing one can think to do above finding the ground state or the other allowed energies of the system is to solve the time dependent Schrödinger equation approximately i.e. in the perturbative manner. Let us apply it to the small destruction effects on the ground state of the quantum system and for the simplicity in one spatial dimension which reduces the kinetic energy operator to the second derivative with the proper coefficients. Let the ground state of the atom, for example the atom of Hydrogen will be such that $$E_0$$ is the smallest of possible values for the eigen-equation:
 * $$H_0 \Psi_0= E_0\Psi_0$$

Let us add the external electric field effect to the Hamiltonian $$H_0$$ in the simplest linear manner so the Schrödinger equation is
 * $$H_0 \Psi(t) - e x f(t)E_0 \sin (\omega t)\Psi(t)= i \hbar \dot \Psi(t)$$.

We will assume $$\Psi(0)=\Psi_0$$ for the initial condition and will check what happens to that state under the influence of the perturbing $$- e x f(t)E_0 \sin (\omega t)$$ term, more specifically where it will go in terms of the expansion in the basis  of the unbound states of the system which in very good approximation are simply plane waves. For the convenience of the calculations we added the $$f(\tau)$$ envelope function normalized to $$1$$ in time so the electric field is turned on and off in the smooth and easy to Fourier transform Gaussian manner:
 * $$f(\tau)=N_1 e^{-(\tau-\tau_0)^2/T_0^2}$$.

it is now convenient to absorb the $$H_0$$ term in the equation in the so-called interaction picture introducing the transformed solution:
 * $$\Psi(t)= e^{-i H_0 t/ \hbar}\Phi(t)$$

The original time-dependent equation greatly simplifies to
 * $$- e x(t) f(t) E_0 \sin (\omega t)\Phi(t)= i \hbar \dot \Phi(t)$$.

where the position operator becomes time dependent namely
 * $$x(t)= e^{i H_0 t/ \hbar} x e^{-i H_0 t /\hbar}$$

With the zero iteration condition $$\Phi(t)=\Psi_0$$ we get in the first approximation
 * $$\Phi(t)= \Psi_0 - \frac{1}{i \hbar}\int_{0}^{t}e f(\tau)E_0 \sin (\omega \tau ) e^{i H_0 \tau / \hbar} x e^{-i H_0 \tau/ \hbar} \Psi_0 d \tau $$

we are now interested in the unbound continuum state component in the final solution which tells us about the energy spectrum of the ionized electrons. We can get that by projecting the solution onto the continuum state, simply:
 * $$E(k)=|\int_{-\infty}^{\infty} <\Psi(x,+\infty)|e^{ik x}>d x|^2$$

where we extended the integration in time from the minus infinity to infinity since the electric field was localized in time with the Gaussian envelope. The only significant term which remains after the integration is:
 * $$E(k)=\frac{e^2 E_0^2}{4 \hbar^2}|<\Psi_0|x]e^{ik x}>{\tilde f}(\hbar^2 k^2/2m - \hbar \omega - E_0)|^2 $$

Where the $$\tilde f $$ is the Fourier transform of the field envelope function $$f$$ and while $$f$$ is broadly localized the $$\tilde f $$ is sharply loalized around the point with the condition
 * $$\hbar^2 k^2/2m - \hbar \omega - E_0=0$$

expressing the energy conservation condition
 * $$E(k)= \hbar^2 k^2/2m = E_0 + \hbar \omega$$

stating that while the ground state energy is negative there is no ionization below the threshold (for the photon or field frequencies that low that the kinetic energy would be impossibly negative) and the ejected electron kinetic energy is equal the energy of the absorbed photon lowered by the ionization or the binding energy.

Example 3: Theory of Above Threshold Ionization (ATI)
Above Threshold Ionization may be explained by solving the time dependent Schrödinger equation in the approximate manner. The Schrödinger equation for the free electron in the field of the electromagnetic wave in one dimension and in the radiation gauge is given by
 * $$\frac{1}{2m}\left(\frac{\hbar}{i}\frac{\partial }{\partial x}-e A(t) \right)^2 \Psi= i\hbar{\frac{\partial \Psi}{\partial t}}$$,

where
 * $$A(t)= \frac{E_0}{\omega}\cos (\omega t)$$

so the electric field is given by
 * $$E(t)= -\frac{\partial A }{\partial t }=E_0 \sin (\omega t)$$

Substituting
 * $$\frac{}{}\Psi(t)=e^{i C(t) + ik x}$$

we are obtaining the equation for $$C(t)$$
 * $$\dot C(t) = \left(\hbar k-e A(t) \right)^2/2m$$

with the solution
 * $$ C(t) =- \frac{\hbar ^2 k^2}{2m }t+\alpha k \sin(\omega t )-\beta \sin(2 \omega t )-\gamma t$$,

where
 * $$\alpha=\frac{(e E_0) \hbar}{m \omega^2}$$
 * $$\beta=\frac{(e E_0)^2}{8 m \omega^3}$$
 * $$\gamma=\frac{ (e E_0)^2}{ 4 m \omega^2}$$.

The Schrödinger equation for the electron in the wave field and in the atomic potential will be given by
 * $$\left[H_0(t) + V(x) \right] \Psi= i\hbar{\frac{\partial \Psi}{\partial t}}$$,

where, $$H_0$$ is the Hamiltonian of the free electron in the field. Adding and subtracting the energy of the ground state from which the electron is to be ionized we obtain
 * $$\left[H_0(t) + V(x) +E_0 - E_0 \right] \Psi= i\hbar{\frac{\partial \Psi}{\partial t}}$$

Because in the ground state the electron kinetic energy is equall the total energy but with the opposite sign (virial theorem) and only this energy will be left after the fast removal of the electron, we neglect in this equation the sum $$v(x)+E_0$$ for all $$x$$ and obtain the approximate equation
 * $$\left[H_0(t) - E_0  \right] \Psi= i\hbar{\frac{\partial \Psi}{\partial t}}$$,

where the only remaining of the atomic potential is the constant.

This equation may now be solved using the previous result  for the free electron in the field and expanding the ground state into its Fourier components
 * $$\Psi(0)=N e^{-|x|/a_0}=\int c_k e^{i k x} dk$$,

with
 * $$c_k =\frac{N}{a_0} \frac{1}{k^2 a_0^2 + 1}$$

This equation has therefore the solution
 * $$\Psi(t)= \int c_k e^{i k x}e^{i E_0 t } e^ {i C(t)} dk $$

We obtain the ionization spectrum from the formula
 * $$E(k)=|\int_{-\infty}^{\infty} <\Psi(\tau)|e^{ik x}>g(\tau) d \tau|^2$$,

telling how much of the plane wave of the free electron with the given kinetic energy is at the and of the ionization process, where $$g(\tau)$$ is the averaging function of the measuring detector for example
 * $$g(\tau)=N_1 e^{-(\tau-\tau_0)^2/T_0^2}$$.

Expanding the factor
 * $$\frac{}{}e^{i \alpha k \sin(\omega t )- i \beta \sin(2 \omega t )}=\sum_n {\mathcal J}_n(-\alpha k,\beta)e^{-i n \omega t}$$

with the generalized Bessel functions $${\mathcal J}_n$$ defined by the inverse transform, we obtain
 * $$E(k)=|\sum_n c_k {\mathcal J}_n(-\alpha k,\beta){\tilde g}(\hbar^2 k^2/2m - n \hbar \omega - E_0 + \gamma)|^2$$

($$\tilde g(\omega)$$ is the Fourier transform of the detector function) therefore the sum of sharp or fuzzy maxima localized around the energy condition of emitted electrons $$\hbar ^2k^2/2m = n \hbar \omega + E_0 - \gamma $$ depending on the speed i.e the averaging parameter of the detector  $$T_0$$.

Example 4: Basic theory of the Trojan Wave Packet
Because the Trojan wave packet is an approximate eigenstate of the Hamiltonian its search starts from the Schrödinger´s equation for the Hydrogen atom in the field of the circularly polarized wave in the coordinate system rotating with the frequency of the field

 * $$H \Psi= E \tfrac{}{}\Psi$$,

where

 * $$H=\frac{2}^2-\frac{r}-  {\epsilon} x- \omega L_z$$,

and $$L_z$$ is the operator of z-component of the angular momentum.

For the simplification one can restrict himself to only two spacial dimensions. This equation after neglecting the curvature terms of the Laplacian and assumption that some terms are slowly varying or even constant takes in the polar coordinate system the simplified and separated form

 * $$\left[ -\frac {\partial^2}{2 \partial r^2} + \frac {l^2}{2 r^2} -\frac {1}{r} - {\epsilon} r -\frac {\partial^2}{2 r_0^2 \partial \phi^2}- {\epsilon} r_0 \cos \phi + \epsilon r_0 \right] \chi = E \chi$$,

 * $$\frac {}{} \chi= e^{il \phi }\Psi,  l = \omega^2 r_0 $$

where $$\hbar=1, m_e=1$$, and $$r_0$$ is the point of the potential of the part of the Hamiltonian dependent only on the radial coordinate and therefore also the radius of the classical orbit. Because the radial potential has the minimum the Trojan wavepacket is in this theory the product of a well localized radial Gaussian function and  a well localized excited state of the quantum mathematical pendulum, corresponding to the pendulum totally reversed upside down which is also the Mathieu function with the characteristic value (and the energy) equal with a good approximation to $$r_0 \epsilon$$. The more precise theory shows that it is the pendulum of a negative and fractional electron mass equal -1/3 (of the electron) and that is why it is on the contrary the ground state with approximately the same energy but in the reversed spectrum.

To notice that let us more keep the correction from the expansion of the centrifugal term

 * $$\Delta H = -2 i \frac {l}{r_0^3}\frac {\partial}{\partial \phi}(r-r_0) $$

and let us consider its action on the Fourier component of $$\chi$$, e.g. $$e^{ik}$$.

The additional centrifugal potential will be

 * $$\Delta V = 2 i \frac {l}{r_0^3} k (r-r_0) $$

It will cause the shift of the minimum and the energy lowering of the radial harmonic oscillator equal to

 * $$\Delta E = -\frac {2}{r_0^2} k^2  $$

Replacing back $$k^2$$ with the operator of the z component of the angular momentum we get

 * $$\Delta H = \frac {2 \partial^2}{ r_0^2 \partial \phi^2}$$

Adding this correction in the Schródinger equation we get the equation with the negative and fractional electron mass -1/3 ($$m_e$$):

 * $$\left[ -\frac {\partial^2}{2 \partial r^2} + \frac {l^2}{2 r^2} -\frac {1}{r} - {\epsilon} r +\frac {3 \partial^2}{2 r_0^2 \partial \phi^2}- {\epsilon} r_0 \cos \phi + \epsilon r_0 \right] \chi = E \chi$$,

which allows the Gaussian localization of the electron in the maximum but not in the minimum of the potential in the angular direction.

Links

 * Above Threshold Ionization photoelectron spectra

Simulations

 * Adiabatic generation of Trojan wave packet from Hydrogen circular state

title: Schrödinger equation


text:
User talk:Mohanganeesh

User page content
Hi there, I noticed that an IP editor (who I assume is you) created your user page. Wikiversity values the ability of contributors to briefly express and describe themselves on their user page. However, may I please remind you that this is the internet, and we strongly advise against uploading personally identifying content - this includes details such as age and mobile number.

As a result, I've removed this from your user page. Anyone can still view it by clicking 'history' at the top, however - if you like, I can have a steward hide the revision entirely and it will disappear forever to all but a select few appointed and trusted explicitly by the wikimedia community.

There aren't any official user page guidelines yet, but I'm sure they'll cover including significant personally identifying content on user pages. We generally don't have a problem with names, locations and all the rest, but beyond a point it can be considered advertising which is against policy. Have fun editing Wikiversity. --Draicone (talk) 22:30, 26 September 2006 (UTC)

title: User talk:Mohanganeesh


text: User:Doc glasgow

title: User:Doc glasgow


text:
User talk:Doc glasgow

__NOINDEX__

try me on en.wikipedia

Request from SB Johnny
Scott,

I got off the phone with SB Johnny a little while ago. He asked me to request that you coordinate with him on his Wikiversity talk page here. Thanks. —Moulton 00:05, 1 March 2011 (UTC)

Thanks
I greatly appreciate your kind words about my contributions.--Poetlister 16:17, 3 June 2011 (UTC)

title: User talk:Doc glasgow


text: User talk:Abresas

title: User talk:Abresas


text: User talk:Truthsolo

title: User talk:Truthsolo


text: User talk:GMonrad

title: User talk:GMonrad


text:
User talk:Bilal.zubairy~enwikiversity

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text: User talk:DivePeak

title: User talk:DivePeak


text:
User talk:Lorenzo~enwikiversity

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text: User talk:GaspardPetit

title: User talk:GaspardPetit


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User talk:Raduga~enwikiversity

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text: User talk:Rupiyaben

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text: User talk:Mail2pradeepc

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User talk:Jirka.benedikt~enwikiversity

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text:
User talk:Yaser Al-Nabriss~enwikiversity

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text: User talk:Aaronm5021

title: User talk:Aaronm5021


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User talk:Naqa inc~enwikiversity

new to wiki?
Are you new to wiki or just new to Wikiversity? Let me know if you need any help. --JWSchmidt 14:38, 2 November 2006 (UTC)

Your account will be renamed
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title: User talk:Naqa inc~enwikiversity


text:
User talk:Barbararana

Image:Musicnotes2.gif
Please provide a license template and source on the image description page. – Mike.lifeguard | @en.wb 23:08, 13 February 2008 (UTC)

title: User talk:Barbararana


text: User talk:I1abnrk

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text: User talk:Hpurcell

title: User talk:Hpurcell


text:
User talk:Cheechako~enwikiversity

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title: User talk:Cheechako~enwikiversity


text: User talk:Jcroxall

title: User talk:Jcroxall


text:
User talk:Amitbhargava~enwikiversity

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title: User talk:Amitbhargava~enwikiversity


text:
User talk:Flubeca~enwikiversity

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title: User talk:Flubeca~enwikiversity


text: User talk:Whobob77

title: User talk:Whobob77


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User talk:Bhadrachalam~enwikiversity

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User talk:Trey~enwikiversity

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text: User talk:Tomkatnan

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User talk:Rayford~enwikiversity

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title: User talk:Rayford~enwikiversity


text: User talk:Rayford8

title: User talk:Rayford8


text: User talk:Charliemurphy25

title: User talk:Charliemurphy25


text:
User talk:Badmuthahubbard~enwikiversity

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title: User talk:Badmuthahubbard~enwikiversity


text:
User talk:Rhys~enwikiversity

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text: User talk:Mdkass

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text: User talk:Ashwani

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User talk:Architpuri~enwikiversity

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title: User talk:Architpuri~enwikiversity


text: User talk:Murili

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text:
User talk:Danellis~enwikiversity

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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 Danellis. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Danellis~enwikiversity 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 23:33, 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) 06:05, 19 April 2015 (UTC)

title: User talk:Danellis~enwikiversity


text: User talk:Dan Ellis

title: User talk:Dan Ellis


text:
User talk:Dedide~enwikiversity

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 Dedide. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Dedide~enwikiversity 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 23:30, 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) 06:05, 19 April 2015 (UTC)

title: User talk:Dedide~enwikiversity


text: User talk:Varunurav

title: User talk:Varunurav


text:
User talk:Eridano~enwikiversity

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 Eridano. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Eridano~enwikiversity 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 23:35, 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) 06:08, 19 April 2015 (UTC)

title: User talk:Eridano~enwikiversity


text: User talk:Khcharan

title: User talk:Khcharan


text:
User talk:Alinak~enwikiversity

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 Alinak. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Alinak~enwikiversity 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 23:27, 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) 06:02, 19 April 2015 (UTC)

title: User talk:Alinak~enwikiversity


text: User talk:Ssmalls

title: User talk:Ssmalls


text: User talk:MindShare

title: User talk:MindShare


text: User talk:J.rodriguez818

title: User talk:J.rodriguez818


text:
User talk:Gonzalo~enwikiversity

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 Gonzalo. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Gonzalo~enwikiversity 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 23:37, 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) 06:09, 19 April 2015 (UTC)

title: User talk:Gonzalo~enwikiversity


text: User talk:Mchl

title: User talk:Mchl


text: User talk:Itwillsting

title: User talk:Itwillsting


text: User talk:Davidnguyen

title: User talk:Davidnguyen


text:
User talk:Aliko~enwikiversity

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 Aliko. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Aliko~enwikiversity 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 23:27, 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) 06:02, 19 April 2015 (UTC)

title: User talk:Aliko~enwikiversity


text: User talk:RaoulMillais

title: User talk:RaoulMillais


text:
User:Draicone/monobook.js

//

$(function { if (wgTitle.indexOf("/") != -1 || document.title.indexOf("- History -") != -1)  //no subpages or history     return;  if (wgCanonicalNamespace == "User" || wgCanonicalNamespace == "User_talk") {     var username = encodeURIComponent( wgTitle );     mw.util.addPortletLink("p-cactions", wgServer + "/wiki/Special:Contributions/" + username, "contribs", "ca-contrib", "User contributions");     mw.util.addPortletLink("p-cactions", "http://tools.wikimedia.de/~interiot/cgi-bin/Tool1/wannabe_kate?username=" + username + "&site=en.wikipedia.org", "count", "ca-editcount", "Edit count from Interiot's Tool1");     mw.util.addPortletLink("p-cactions", "http://www.math.ucla.edu/~aoleg/wp/rfa/edit_summary.cgi?user=" + username + "&site=en.wikipedia.org", "Summary", "ca-summary", "Edit Summary");  } });

//

// Helper tools mw.loader.load(            'https://en.wikipedia.org/w/index.php?title=User:Voice_of_All/Addtabs/monobook.js'             + '&action=raw&ctype=text/javascript&dontcountme=s'); // // Admin tools document.write(' '); // // Log tools document.write(' ');

// mw.loader.load('//meta.wikimedia.org/w/index.php?title=User:Krinkle/RTRC.js&action=raw&ctype=text/javascript');

document.write(' ');

title: User:Draicone/monobook.js


text:
User:Draicone/monobook.css

/*  * Begin duplicate tabs * If you would like duplicate tabs as well, copy everything * from here to the next comment block into your monobook.css */ margin: -0.3em 0 0 11.5em; white-space:nowrap; line-height: 1.1em; overflow: visible; border-collapse: collapse; padding: 0 0 0 1em; list-style: none; font-size: 95%; } display: inline; border: 1px solid #aaaaaa; border-top: none; padding: 0.1em 0 0 0; margin: 0 0.3em 0 0; overflow: visible; background: White; } border-color: #fabd23; padding: 0.2em 0 0 0; } background-color: White; color: #002bb8; border: none; padding: 0.3em 0.8em 0 0.8em; text-decoration: none; text-transform: lowercase; position: relative; margin: 0; } z-index: 3; text-decoration: none; } padding-left: 0.4em; padding-right: 0.4em; } li#mytabs-ca-talk { margin-right: 1.6em; } li#mytabs-ca-watch, li#mytabs-ca-unwatch, li#mytabs-ca-varlang-0, li#mytabs-ca-print { margin-left: 1.6em; } /* // End duplicate tabs */ /* Floating sidebar commented out for now - breaking layout. div[id=column-one] { position: fixed; height: 100%; overflow: auto; z-index: 2; } height: 10em; overflow: auto; } body { background-attachment: fixed; } margin-left: 13.6em; border-left: solid 1px rgb(250, 189, 35); } position:relative; z-index:3; width: 11.6em; } width: 10.7em; border: none; margin: 0 0 0.1em 0em; float: none; overflow: hidden; font-size: 95%; background: White; border-collapse: collapse; border: 1px solid #aaaaaa; padding: 0 0.8em 0.3em .5em; } line-height: 1.5em; list-style-type: square; list-style-image: url("/style/monobook/bullet.gif"); font-size:95%; margin: 0 0 0 1.5em; padding:0; text-align:left; text-transform: none; } display: list-item; padding:0; margin: 0 0 0 0; margin-bottom: 0.1em; } li#pt-userpage { background: none } */ // End comment out of floating sidebar
 * 1) mytabs {
 * 1) mytabs .hiddenStructure { display: none; }
 * 2) mytabs li {
 * 1) mytabs li.selected {
 * 1) mytabs li a {
 * 1) mytabs li.selected a { z-index: 3; }
 * 2) mytabs .new a { color:#ba0000; }
 * 3) mytabs li a:hover {
 * 1) mytabs h5 { display: none; }
 * 2) mytabs li.istalk { margin-right: 0; }
 * 3) mytabs li.istalk a { padding-right: 0.5em; }
 * 4) mytabs-ca-addsection a {
 * 1) p-lang .pBody ul{
 * 1) footer {
 * 1) p-personal {
 * 1) p-personal .pBody {
 * 1) p-personal ul {
 * 1) p-personal li {

title: User:Draicone/monobook.css


text:
User:879(CoDe)~enwikiversity

879(CoDe) 00:48, 27 September 2006 (UTC)

title: User:879(CoDe)~enwikiversity


text:
User talk:879(CoDe)~enwikiversity

User page + Help desk Q
Please do not put excessive repeated content on your user page (or any other page, for that matter). Users on slow connections or computers with less memory can have problems accessing the site and it can even result in legal action against the Wikimedia Foundation. Your user page is designed to allow users to briefly describe themselves and express themself. Also, I have replied to your question at the help desk. Have fun editing Wikiversity. --Draicone (talk) 01:13, 27 September 2006 (UTC)

Invitation
Dear user of Wikiversity,

Do you like to join a reading club, where you can read and discuss literature? Reading clubs could have active and inactive participants. Active participants could be required to edit on a regularly basis untill a deadline is reached and another topic can be chosen for reading and discussing. Hopefully, reading clubs can ensure a social network on Wikiversity of people cooperating with eachother and becoming friends while discussing knowledge.--Daanschr 09:19, 1 November 2007 (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 879(CoDe). To make sure that both of you can use all Wikimedia projects in future, we have reserved the name 879(CoDe)~enwikiversity 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 23:26, 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) 06:01, 19 April 2015 (UTC)

title: User talk:879(CoDe)~enwikiversity


text: Category:Flash ActionScript

title: Category:Flash ActionScript