Help with simple numerical ODE problem from QM

mistergrinch

Here's a simple numerical analysis problem that is confusing me. Can someone help me understand what boundary conditions to use here?

f''(x) - (x^2 - E_n) * f(x) = 0;

Assume f -> 0 as x -> +- inf. This equation comes from Schrodinger's equation for a one dimensional trapping potential, with E_n proportional to energy.

I am supposed to find the first five eigenvalues and eigenvectors with a shooting method, using x in [-4,4], and normalizing f so that int(f^2) = 1;

I'm not given any boundary conditions, so I'm not sure how to solve this problem. Can anyone help me understand what is going on here? Thanks!

HallsofIvy

If you are asked to find eigenvalues, then your boudary conditions have to be y(-4)= y(4)= 0.