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!