5.2. (a) Find an expression for the energy levels of a three-dimensional harmonic oscillator. This should be described in most introductory quantum mechan ies texts. Do not actually solve Schrödinger's equation for this problem, The three-dimensional harmonic oscillator potential is widely used as an approximation for the shell model potential, not because it is particularly accurate, but because it is simple and convenient. (b) Draw an energy level diagram for these energy levels and determme the degeneracy of each level. (e) Use this model to predict the magic numbers for the system.

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