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Journal of Atomic and Molecular Physics

Recurrence formula for radial matrix elements of N-dimensional isotropic harmonic oscillator

Shouxin Cui

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

The isotropic harmonic oscillator is one of the potential fields with strict solution.There is important significance to discuss and study it in theory and application.In this paper the recurrence formula for radial matrix elements 〈n_rl｜r~k｜n′_rl′〉 of N-dimensional isotropic harmonic oscillator is derived and on the basis of it we obtain the recurrence formula for the expectation values.We discuss the common property of the recurrence formula for radial matrix elements,however,in Refs[3] and [4] the recurrence formula for radial matrix elements are only the examples of the result in this paper.

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The isotropic harmonic oscillator is one of the potential fields with strict solution.There is important significance to discuss and study it in theory and application.In this paper the recurrence formula for radial matrix elements 〈n_rl｜r~k｜n′_rl′〉 of N-dimensional isotropic harmonic oscillator is derived and on the basis of it we obtain the recurrence formula for the expectation values.We discuss the common property of the recurrence formula for radial matrix elements,however,in Refs[3] and [4] the recurrence formula for radial matrix elements are only the examples of the result in this paper.