mistergrinch
Oct23-09, 11:18 PM
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!
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!