Energies and wave functions for infinite wall at x=0 with harmonic potential for x>0

[hamilton5]

Homework Statement

What are the energies and wave functions for the quantum mechanical model where V = infinity for x less than or equal to 0 and V = kx²/2 for x greater than or equal to 0?

Homework Equations

1-D particle in a box E = (h²/8m)(n²/L²)

Harmonic Oscillator E = (v + 1/2)(h/2*pi)w

The Attempt at a Solution

Honestly, I had no clue where to start. This was the last problem on our first exam. I tried drawing what it would represent graphically but I'm not really sure what I was supposed to answer... Do I add the energies together? Wave functions? I'm not even sure what format our professor was looking for he didn't tell us...

 

[vela]

Solve the Schrödinger equation in each region, x<0 and x>0, and then join the solutions at x=0.