A Modern Approach to Quantum Mechanics · Problem 10.16

Time-Independent Perturbations — John S. Townsend

Physics — Quantum Mechanics · anisotropic-harmonic-oscillator

Problem

The potential energy in a particular anisotropic harmonic oscillator with cylindrical symmetry is given by V=12μ[ω12(x2+y2)+ω32z2]V = \frac{1}{2}\mu[\omega_1^2(x^2 + y^2) + \omega_3^2 z^2] with ω1<ω3<2ω1\omega_1 < \omega_3 < 2\omega_1. (a) Determine the energy eigenvalues and the degeneracies of the three lowest energy levels by using Cartesian coordinates. (b) Solve the energy eigenvalue equation in cylindrical coordinates and check your results in comparison with those of (a).

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