This Demonstration shows solutions of the one-dimensional Schrödinger equation in a multi-step potential well, confined between
. The controls on the left determine the heights and widths of the segments of the potential well. Select a quantum number
(from 1 to 20) to plot the
eigenfunction of the Schrödinger equation
. The Schrödinger equation is then solved numerically using Mathematica's built-in function NDEigensystem
. Energies are expressed in units of
. The wavefunctions are plotted in red, in arbitrary units, with the black curves showing the corresponding probability densities.