Consider the three-dimensional harmonic oscillator, for which the potential is V ( r ) = 1/2 m 2 r 2 (a) Show that the

Consider the three-dimensional harmonic oscillator, for which the potential is

V ( r ) = 1/2 m ω² r² 

(a) Show that the separation of variables in Cartesian coordinates turns this into three one-dimensional oscillators, and exploit your knowledge of the latter to determine the allowed energies. 

Answer: E_n = ( n + 3/2 ) ħ ω

(b) Determine the degeneracy d ( n ) of E_n