File:Quantum Harmonic Oscillator Levels.png

DescriptionQuantum Harmonic Oscillator Levels.png	English: A diagram showing wavefunction of a quantum harmonic oscillator for energy levels n = 0 to 20. The probability density is shown by the colour, black is the lowest, white is the highest.
Date	19 April 2009
Source	Own work
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

(*QHO wavefunction*)
psi[n_, x_] := Exp[-x^2/2] / Sqrt[2^n *n!*Sqrt[Pi]]*HermiteH[n, x];

(*Colour function*)
colourFunc[x_] := (Blend[{Black, Red, Yellow, White}, x*1.8] &);

(*Generates a single strip showing one QHO energy level wavefunction*)
level[n_] := DensityPlot[
   psi[n, x]^2,
   {x, -8, 8},
   {y, 0, 1},
   PlotRange -> {0, 0.7},
   PlotPoints -> {100, 2},
   Frame -> False,
   ColorFunction -> colourFunc[#],
   AspectRatio -> 1/32,
   ImageSize -> 1600,
   Method -> {"ShrinkWrap" -> True},(*Remove whitespace at edges*)
   ColorFunctionScaling -> False (*Have a consistent CF scaling*)
   ];

(*Assemble the entire drawing of all levels*)
graphic = GraphicsGrid[ 
  Reverse[Table[
    {level[k]},
    {k, 0, 20}]],
  Spacings -> 0]