Wolfram Language

Partial Differential Equations

Study Dispersion in Quantum Mechanics

Solve the one-dimensional Schrödinger equation for a free particle that is initially strongly localized around .

Click for copyable input
eqn = I D[\[Psi][x, t], t] == D[\[Psi][x, t], {x, 2}]; sol[x_, t_] = DSolveValue[{eqn, \[Psi][x, 0] == Exp[-x^2]}, \[Psi][x, t], {x, t}]

As time increases, the wavefunction becomes less sharply peaked at the origin.

Click for copyable input
Manipulate[ Plot[Abs@sol[x, t], {x, -10, 10}, PlotRange -> {0, 1}, PlotTheme -> "Scientific", ImageSize -> Medium], {t, 0, 5, Appearance -> "Labeled"}]
Play Animation
Stop Animation

Related Examples

de es fr ja ko pt-br ru zh