Question

write down degeneracy for isotropic 2 d harmonic oscillator.

Answer 1

The degeneracy of k-dimentional harmonic oscillator is given by

$\displaystyle g(n,k) = \frac{(n+k-1)!}{n!(k-1)!}$

where n is the n-th energy level.

So, for 2D harmonic oscillator one obtains

$\displaystyle g(n,2)= \frac{(n+1)!}{n! } = n+1$