# Degenracy of quantum osscilator

1. Apr 8, 2007

### Lee

1. The problem statement, all variables and given/known data
Why does the degeneracy of the first 4 energy's of the quantum harmonic oscillator differ when considering the solution in Cartesian and spherical polars.

2. Relevant equations
For cart.
E=h(bar)w(nx+ny+nz+3/2)
For spherical polars
E=h(bar)w(n+3/2) where n=l+j, where j is even.

3. The attempt at a solution

The solution in Cartesian co ordinates depends on 3 independent variables where as the the spherical polar co ordinates we have a independent variable r and the azimuthal and radial parts are linked.

Is this correct?