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English: Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state , which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called "stationary states".
Thus in every quantum stae,there are certain preferred positions of maximum probability
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Sbyrnes321
(* Source code written in Mathematica 6.0 by Steve Byrnes, Feb. 2011. This source code is public domain. *) (* Shows classical and quantum trajectory animations for a harmonic potential. Assume m=w=hbar=1. *) ClearAll["Global`*"] (*** Wavefunctions of the energy eigenstates ***) psi[n_, x_] := (2^n*n!)^(-1/2)*Pi^(-1/4)*Exp[-x^2/2]*HermiteH[n, x]; energy[n_] := n + 1/2; psit[n_, x_, t_] := psi[n, x] Exp[-I*energy[n]*t]; (*** A non-stationary state ***) SeedRandom[1]; psinonstationary[x_, t_] := (psit[0, x, t]+psit[1, x, t])/Sqrt[2]; (*** Put all the plots together ***) SetOptions[Plot, {PlotRange -> {-1, 1}, Ticks -> None, PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Pink]}}]; MakeFrame[t_] := GraphicsGrid[ {{Plot[{Re[psit[0, x, t]], Im[psit[0, x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],0]], Plot[Abs[psit[0, x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black], PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],0]]^2]]}, {Plot[{Re[psit[1, x, t]], Im[psit[1, x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],1]], Plot[Abs[psit[1, x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black], PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],1]]^2]]}, {Plot[{Re[psinonstationary[x, t]], Im[psinonstationary[x, t]]}, {x, -5, 5}, PlotLabel -> Subscript[\[Psi],N]], Plot[Abs[psinonstationary[x, t]]^2, {x, -5, 5}, PlotStyle -> Directive[Thick, Black], PlotLabel -> TraditionalForm[Abs[Subscript[\[Psi],N]]^2]]} }, Frame -> All, ImageSize -> 300]; output = Table[MakeFrame[t], {t, 0, 4 Pi*40/41, 4 Pi/41}]; SetDirectory["C:\\Users\\Steve\\Desktop"] Export["test.gif", output]
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{{Information |Description ={{en|1=Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the partic
fayl, stationarystatesanimation, fayl, faylın, tarixçəsi, istifadə, edilən, səhifələr, faylın, qlobal, istifadəsidaha, yüksək, versiyası, yoxdur, stationarystatesanimation, 8206, piksel, fayl, həcmi, mime, növü, image, ilmələnib, çərçivə, fayl, vikimedia, comm. Fayl Faylin tarixcesi Istifade edilen sehifeler Faylin qlobal istifadesiDaha yuksek versiyasi yoxdur StationaryStatesAnimation gif 8206 300 280 piksel fayl hecmi 223 KB MIME novu image gif ilmelenib 41 cercive Bu fayl Vikimedia Commons dadirve diger layihelerde istifade edile biler Faylin tesvir sehifesine get Xulase IzahStationaryStatesAnimation gif English Three wavefunction solutions to the Time Dependent Schrodinger equation for a harmonic oscillator Left The real part blue and imaginary part red of the wavefunction Right The probability of finding the particle at a certain position The top two rows are the lowest two energy eigenstates and the bottom is the superposition state ps N ps 0 ps 1 2 displaystyle psi N psi 0 psi 1 sqrt 2 which is not an energy eigenstate The right column illustrates why energy eigenstates are also called stationary states Thus in every quantum stae there are certain preferred positions of maximum probabilityTarix 20 mart 2011Menbe Oz isiMuellif Sbyrnes321 Source code written in Mathematica 6 0 by Steve Byrnes Feb 2011 This source code is public domain Shows classical and quantum trajectory animations for a harmonic potential Assume m w hbar 1 ClearAll Global Wavefunctions of the energy eigenstates psi n x 2 n n 1 2 Pi 1 4 Exp x 2 2 HermiteH n x energy n n 1 2 psit n x t psi n x Exp I energy n t A non stationary state SeedRandom 1 psinonstationary x t psit 0 x t psit 1 x t Sqrt 2 Put all the plots together SetOptions Plot PlotRange gt 1 1 Ticks gt None PlotStyle gt Directive Thick Blue Directive Thick Pink MakeFrame t GraphicsGrid Plot Re psit 0 x t Im psit 0 x t x 5 5 PlotLabel gt Subscript Psi 0 Plot Abs psit 0 x t 2 x 5 5 PlotStyle gt Directive Thick Black PlotLabel gt TraditionalForm Abs Subscript Psi 0 2 Plot Re psit 1 x t Im psit 1 x t x 5 5 PlotLabel gt Subscript Psi 1 Plot Abs psit 1 x t 2 x 5 5 PlotStyle gt Directive Thick Black PlotLabel gt TraditionalForm Abs Subscript Psi 1 2 Plot Re psinonstationary x t Im psinonstationary x t x 5 5 PlotLabel gt Subscript Psi N Plot Abs psinonstationary x t 2 x 5 5 PlotStyle gt Directive Thick Black PlotLabel gt TraditionalForm Abs Subscript Psi N 2 Frame gt All ImageSize gt 300 output Table MakeFrame t t 0 4 Pi 40 41 4 Pi 41 SetDirectory C Users Steve Desktop Export test gif output Lisenziya I the copyright holder of this work hereby publish it under the following license This file is made available under the Creative Commons CC0 1 0 Universal Public Domain Dedication The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law including all related and neighboring rights to the extent allowed by law You can copy modify distribute and perform the work even for commercial purposes all without asking permission http creativecommons org publicdomain zero 1 0 deed en CC0 Creative Commons Zero Public Domain Dedication false falseCaptionsazerbaycancaAdd a one line explanation of what this file representsItems portrayed in this filetesvir ediryaradiciSome value without a Vikiverilenler itemmuellifin qisa adi Sbyrnes321Wikimedia username ingilis Sbyrnes321URL ingilis https commons wikimedia org wiki user Sbyrnes321copyright status ingiliscopyrighted dedicated to the public domain by copyright holder ingiliscopyrighted ingilislisenziyaCC0 ingilissource of file ingilisoriginal creation by uploader ingilisyaranma tarixi20 mart 2011 Faylin tarixcesi Faylin evvelki versiyasini gormek ucun gun tarix bolmesindeki tarixlere klikleyin Tarix VaxtKicik sekilOlculerIstifadeciSerh indiki18 21 20 mart 2011300 280 223 KB Sbyrnes321 Information Description en 1 Three wavefunction solutions to the Time Dependent Schrodinger equation for a harmonic oscillator Left The real part blue and imaginary part red of the wavefunction Right The probability of finding the partic Istifade edilen sehifeler Bu sekile olan kecidler Sredinger tenliyi Faylin qlobal istifadesi Bu fayl asagidaki vikilerde istifade olunur ar wikipedia org layihesinde istifadesi معادلة شرودنغر حالة مستقرة فيزياء رياضية بوابة ميكانيكا الكم صور مختارة بوابة ميكانيكا الكم صور مختارة 3 ast wikipedia org layihesinde istifadesi Ecuacion de Schrodinger bn wikipedia org layihesinde istifadesi গ ণ ত ক পদ র থব জ ঞ ন bs wikipedia org layihesinde istifadesi Stacionarno stanje de wikipedia org layihesinde istifadesi Ubergangsdipolmoment en wikipedia org layihesinde istifadesi Schrodinger equation Mathematical physics Stationary state Transition dipole moment User Sbyrnes321 User VGrigas WMF Quality Media eo wikipedia org layihesinde istifadesi Matematika fiziko es wikipedia org layihesinde istifadesi Ecuacion de Schrodinger fa wikipedia org layihesinde istifadesi ریاضی فیزیک ga wikipedia org layihesinde istifadesi Fisic mhatamaiticiuil hy wikipedia org layihesinde istifadesi Շրյոդինգերի հավասարում ia wikipedia org layihesinde istifadesi Equation de Schrodinger id wikipedia org layihesinde istifadesi Fisika matematis Persamaan Schrodinger Fungsi gelombang ja wikipedia org layihesinde istifadesi シュレーディンガー方程式 遷移双極子モーメント mk wikipedia org layihesinde istifadesi Matematichka fizika Shredingerova ravenka pa wikipedia org layihesinde istifadesi ਗਣ ਤ ਕ ਭ ਤ ਕ ਵ ਗ ਆਨ ਸ ਰ ਡ ਜਰ ਇਕ ਏਸ ਨ pl wikipedia org layihesinde istifadesi Rownanie Schrodingera Stan stacjonarny fizyka pnb wikipedia org layihesinde istifadesi شروڈنگر مساوات ro wikipedia org layihesinde istifadesi Fizică matematică sl wikipedia org layihesinde istifadesi Matematicna fizika ta wikipedia org layihesinde istifadesi ச ர ட ங கர சமன ப ட tl wikipedia org layihesinde istifadesi Ekwasyong Schrodinger Pisikang matematikal tr wikipedia org layihesinde istifadesi Schrodinger denklemi uk wikipedia org layihesinde istifadesi Rivnyannya Shredingera vi wikipedia org layihesinde istifadesi Vật ly toan học www wikidata org layihesinde istifadesi Q165498 zh wikipedia org layihesinde istifadesi 波函数 定態 Menbe https az 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