A Modern Approach to Quantum Mechanics · Problem 10.12

Time-Independent Perturbations — John S. Townsend

Physics — Quantum Mechanics · isotropic-oscillator-power-series

Problem

(a) Substitute the expression (10.93) for the radial wave function of the three-dimensional isotropic oscillator into (10.91) to determine the differential equation that f(ρ)f(\rho) obeys. (b) Obtain a two-term recursion relation for the power series (10.94); show that this power series must terminate and that the energy eigenvalues of the oscillator are given by (10.95).

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