## Help with simple numerical ODE problem from QM

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!
 PhysOrg.com science news on PhysOrg.com >> Leading 3-D printer firms to merge in $403M deal (Update)>> LA to give every student an iPad;$30M order>> CIA faulted for choosing Amazon over IBM on cloud contract
 Recognitions: Gold Member Science Advisor Staff Emeritus If you are asked to find eigenvalues, then your boudary conditions have to be y(-4)= y(4)= 0.

 Similar discussions for: Help with simple numerical ODE problem from QM Thread Forum Replies Calculus & Beyond Homework 2 Classical Physics 4 Engineering, Comp Sci, & Technology Homework 9 Calculus & Beyond Homework 4 Introductory Physics Homework 2