Consider the three-dimensional harmonic oscillator, for which the potential is V(r) = 1/2m omega2 r2. [4.188] Show that 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)h omega. [4.189] Determine the degeneracy d(n) of En.