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Journal of Xuzhou Normal University

Recurrence Formula for Radial Matrix Elements of Two-dimensional Isotropic Harmonic Oscillator

Yao-Min Di

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

The recurrence formula for radial matrix elements of two-dimensional isotropic harmonic oscillator is derived. On the basis the recurrence relation for average value is obtained,and the parameter relation between two- and three-dimensional isotropic harmonic oscillators is discussed.

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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.