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 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?

Transcribed Image Text:

VImn (x) = w1(x) m(y)V »(z)