This Demonstration calculates eigenvalues and eigenfunctions for the perturbed Schrödinger equation

with

, where

. Units are

. The energies and wavefunctions for the unperturbed potential

are given by

and

, where

is a Hermite polynomial. When you select "

", the numerical solution for

and the unperturbed solution

are plotted. When you select "

",

is plotted. When you select "

",

is shown as a solid black line,

as a dashed red curve and

as a blue curve. The unperturbed eigenvalue is given by

in all cases.