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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: En = ( n + 3/2 ) ħ ω

 

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

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