File:QM orbital evolution.gif
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Captions
Captions
Time evolution of 2 hydrogen atom orbitals
Summary
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| Description |
English: "Orbitals" are eigenstates of a quantum system, but that doesn't mean that the wavefunction does not evolve with time. The modulus of the wavefunction stays constant, but its real and imaginary parts don't.
In particular, orbitals with m≠0 have their real and imaginary parts rotate out of phase with each other. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1107313759461224449 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
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\[Alpha]0 = 1;
\[Psi][n_, l_, m_, r_, \[Theta]_, \[Phi]_, t_] := Sqrt[(2/(n \[Alpha]0))^3 (n - l - 1)!/(2 n ((n + l)!))] E^(-r/(n \[Alpha]0)) ((2 r)/(n \[Alpha]0))^l LaguerreL[n - l - 1, 2 l + 1, (2 r)/(n \[Alpha]0)] SphericalHarmonicY[l, m, \[Theta], \[Phi]] E^(I 2 \[Pi] t);
p1 = Table[Grid[{
{Text["State"], Text["|\[Psi]|"], Text["Re[\[Psi]]"], Text["Im[\[Psi]]"]},
{Text["|2,1,1>"],
f =
TransformedField["Spherical" -> "Cartesian", \[Psi][2, 1, 1, r, \[Theta], \[Phi], t], {r, \[Theta], \[Phi]} -> {x, y, z}];
DensityPlot3D[Abs[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
,
DensityPlot3D[Re[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
,
DensityPlot3D[Im[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
},
{Text["|3,2,1>"], f = TransformedField["Spherical" -> "Cartesian", \[Psi][3, 2, 1, r, \[Theta], \[Phi], t], {r, \[Theta], \[Phi]} -> {x, y, z}];
DensityPlot3D[Abs[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
,
DensityPlot3D[Re[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
,
DensityPlot3D[Im[f], {x, -20, 20}, {y, -20, 20}, {z, -20, 20}, ColorFunction -> Hue, ColorFunctionScaling -> True, Boxed -> False, Axes -> False]
}
}]
, {t, 0, 1, 0.05}];
ListAnimate[p1]
Licensing
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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.
|
|
This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1107313759461224449, was reviewed on 18 March 2019 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.
|
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:01, 18 March 2019 | | 616 × 420 (1.22 MB) | Berto (talk | contribs) | User created page with UploadWizard |
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