Question: Show that the solution to Schr?dinger?s equation for a three-dimensional harmonic oscillator is? where ? n (x) is a solution to the one-dimensional oscillator with

Show that the solution to Schr?dinger?s equation for a three-dimensional harmonic oscillator is?

VImn (x) = w1(x) m(y)V (z)

where ?_n(x) is a solution to the one-dimensional oscillator with energy (n + 1/2)??. Show that the energies of the three-dimensional oscillator are (N + 3/2)?? for N = 0, 1, 2, . . . and find the degeneracies of the first four energy levels. Do you recognize the sequence?

VImn (x) = w1(x) m(y)V (z)

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