Introduction to Quantum Mechanics · Problem 4.46

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · 3d_harmonic_oscillator

Problem

Consider the three-dimensional harmonic oscillator, for which the potential is V(r)=12mω2r2V(r) = \frac{1}{2}m\omega^2 r^2. (4.215) (a) 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+32)ℏωE_n = \left(n + \frac{3}{2}\right)\hbar\omega. (4.216) (b) Determine the degeneracy d(n)d(n) of EnE_n.

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