Datoteka:QuantumHarmonicOscillatorAnimation.gif
Prijeđi na navigaciju
Prijeđi na pretragu
Veća rezolucija nije dostupna.
QuantumHarmonicOscillatorAnimation.gif (300 × 373 piksela, veličina datoteke/fajla: 759 KB, MIME tip: image/gif, stalno iznova, 97 sličica)
Sažetak
| Opis |
English: A harmonic oscillator in classical mechanics (A-B) and quantum mechanics (C-H). In (A-B), a ball, attached to a spring (gray line), oscillates back and forth. In (C-H), wavefunction solutions to the Time-Dependent Schrödinger Equation are shown for the same potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (C,D,E,F) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (G-H) are non-stationary states, solutions to the Time-Dependent but not Time-Independent Schrödinger Equation. (G) is a randomly-generated superposition of the four states (E-F). H is a "coherent state" ("Glauber state") which somewhat resembles the classical state B.
العربية: مذبذب توافقي في الميكانيكا الكلاسيكية (A-B) وميكانيكا الكم (C-H). في (A-B)، كرة متصلة بنابض (خط رمادي)، تتأرجح ذهابًا وإيابًا. في (C-H)، يعرض حلول الدالة الموجية لمعادلة شرودنغر المعتمدة على الوقت لنفس الإمكانات. المحور الأفقي هو الموضع، والمحور العمودي هو الجزء الحقيقي (الأزرق) أو الجزء التخيلي (الأحمر) من دالة الموجة. (C ،D ،E ،F) هي حالات ثابتة (حالات الطاقة الذاتية)، والتي تأتي من حلول معادلة شرودنغر المستقلة عن الزمن. (G-H) هي حالات غير ثابتة، وهي حلول لمعادلة شرودنغر التي تعتمد على الوقت ولكنها ليست مستقلة عن الوقت. (G) هو تراكب أنشىء عشوائيًا للحالات الأربع (E-F). H هي "حالة متماسكة" ("حالة جلوبر") تشبه إلى حد ما الحالة الكلاسيكية B. |
| Datum | |
| Izvor | Vlastito djelo |
| Autor | 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 random time-dependent state ***)
SeedRandom[1];
CoefList = Table[Random[]*Exp[2 Pi I Random[]], {n, 0, 4}];
CoefList = CoefList/Norm[CoefList];
Randpsi[x_, t_] := Sum[CoefList[[n + 1]]*psit[n, x, t], {n, 0, 4}];
(*** A coherent state (or "Glauber state") ***)
CoherentState[b_, x_, t_] := Exp[-Abs[b]^2/2] Sum[b^n*(n!)^(-1/2)*psit[n, x, t], {n, 0, 15}];
(*** Make the classical plots...a red ball anchored to the origin by a gray spring. ***)
classical1[t_, max_] := ListPlot[{{max Cos[t], 0}}, PlotStyle -> Directive[Red, AbsolutePointSize[15]]];
zigzag[x_] := Abs[(x + 0.25) - Round[x + 0.25]] - .25;
spring[x_, left_, right_] := (.9 zigzag[3 (x - left)/(right - left)])/(1 + Abs[right - left]);
classical2[t_, max_] := Plot[spring[x, -5, max Cos[t]], {x, -5, max Cos[t]}, PlotStyle -> Directive[Gray, Thick]];
classical3 = ListPlot[{{-5, 0}}, PlotStyle -> Directive[Black, AbsolutePointSize[7]]];
classical[t_, max_, label_] := Show[classical2[t, max], classical1[t, max], classical3,
PlotRange -> {{-5, 5}, {-1, 1}}, Ticks -> None, Axes -> {False, True}, PlotLabel -> label, AxesOrigin -> {0, 0}];
(*** Put all the plots together ***)
SetOptions[Plot, {PlotRange -> {-1, 1}, Ticks -> None, PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Pink]}}];
MakeFrame[t_] := GraphicsGrid[
{{classical[t + 2, 1.5, "A"], classical[t, 3, "B"]},
{Plot[{Re[psit[0, x, t]], Im[psit[0, x, t]]}, {x, -5, 5}, PlotLabel -> "C"],
Plot[{Re[psit[1, x, t]], Im[psit[1, x, t]]}, {x, -5, 5}, PlotLabel -> "D"]},
{Plot[{Re[psit[2, x, t]], Im[psit[2, x, t]]}, {x, -5, 5}, PlotLabel -> "E"],
Plot[{Re[psit[3, x, t]], Im[psit[3, x, t]]}, {x, -5, 5}, PlotLabel -> "F"]},
{Plot[{Re[Randpsi[x, t]], Im[Randpsi[x, t]]}, {x, -5, 5}, PlotLabel -> "G"],
Plot[{Re[CoherentState[1, x, t]], Im[CoherentState[1, x, t]]}, {x, -5, 5}, PlotLabel -> "H"]}
}, Frame -> All, ImageSize -> 300];
output = Table[MakeFrame[t], {t, 0, 4 Pi*96/97, 4 Pi/97}];
SetDirectory["C:\\Users\\Steve\\Desktop"]
Export["test.gif", output]
Licenciranje
Ja, vlasnik autorskog prava ovog djela, ovdje ga objavljujem pod sljedećom licencom:
 
|
Ova datoteka je dostupna pod licencom Creative Commons CC0 1.0 Univerzalnom Posvetom Javne Domene. |
| Osoba koja je učestvovala u radu na ovom dokumentu posvetila je rad javnoj domeni odricanjem od svih svojih prava na taj rad širom svijeta po zakonu o autorskim pravima i svim povezanim zakonskim pravima koja bi imao/imala, u mjeri dopuštenoj zakonom. Možete kopirati, mijenjati, distribuirati i prilagođavati rad, čak i u komercijalne svrhe, bez traženja dopuštenja.
|
Historija datoteke
Kliknite na datum/vrijeme da biste vidjeli tadašnju verziju datoteke.
| Datum/vrijeme | Minijatura | Dimenzije | Korisnik | Komentar | |
|---|---|---|---|---|---|
| aktualna | 2. marta 2011. u 10:16 | | 300 × 373 (759 KB) | wikimediacommons>Sbyrnes321 | Alter spring, to avoid the visual impression that the ball is rotating in a circle around the y-axis through the third dimension. |
Upotreba datoteke
Sljedeća stranica koristi ovu datoteku:
