Eigenvalues/functions for hamiltonian in 1D harmonic oscillator

[Csuiter]

Homework Statement

Find the eigenvalues and eigenfunctions of H\hat{} for a 1D harmonic oscillator system with V(x) = infinity for x<0, V(x) = 1/2kx^2 for x > or equal to 0.

Homework Equations

The Attempt at a Solution

I think the hamiltonian is equal to the potential + kinetic energy. I am pretty confused right now. I do ok in class but I had to miss a few days and I am lost.

 

[diazona]

To start with: do you know how to find the eigenvalues and eigenfunctions of the regular harmonic oscillator, which has a potential
V(x) = \frac{1}{2}kx^2
for all x (less than, greater than, and equal to zero)? If not, you really need to learn that first.