# Homework Help: Observable $$G_{z}= -(xL_x+yL_y)$$

1. Apr 15, 2010

### castlemaster

1. The problem statement, all variables and given/known data

Consider the space of the states of a particle with no spin under an isotropic harmonic oscillator potential and the observable $$G_{z}= -(xL_x+yL_y)$$
Obtain the spectrum of Gz. Will be ever he particle in a normalisable state where Gz is defined?

Can you interpret phisically Gz?

2. Relevant equations

3. The attempt at a solution

I think $$G_{z}= zL_z$$

but how do I calculate the possible values of the observable.I tried with anhilitation and creation operators, but what represents Gz?

Thanks