Find an eigenfunction for the finite square well eigenproblem , , y(x)0, where is a square well potential of height 5.

Start by plotting solutions of for :
The true eigenfunctions satisfy y(x)0. These can be approximated by finding functions with . Because the equation is symmetric in , only solutions with need to be found. Plot for :
The root is the approximate eigenvalue:
Plot the approximate eigenfunction together with solutions for nearby :