3D oscillator trapped away from centre

[ftft]

The spherical oscillator problem is for a potential centered at the origin.. but what if the particle is confined to oscillate at a small shift by a small (not infinite) barrier? The potential is now centered about the new position.. Could someone please suggest a way to solve the problem for the energy levels?

 

[Vanadium 50]

Can you write down the potential?

 

[ftft]

I assume the general form of the potential is
1/2 m w^2 (r-r0)^2

 

[Vanadium 50]

Then it can be solved using a change of variables,