Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Moments of the radial density distribution

Naeem Ullah

Published Aug 7, 1989• 0 citations
Publisher

Abstract

The matrix elements of powers of r 2 are evaluated in the basis of radial wavefunctions of a three-dimensional harmonic oscillator as a terminating type of generalised hypergeometric function 3 F 2 . They are employed to calculate the low-order moments of the radial density distribution. The form of radial density distribution for large values of oscillator quanta are given.

DOI
10.1088/0305-4470/22/15/013

Related papers

A briefly form of radial matrix eiement〈n_r'l'm'|r~p|n_rlm〉 in three-dimensional harmonic oscillator energy representation

Zhongshi Li

The radial matrix element〈nr'l'm'|rp|nrlm〉 is derived in a brief form in the three-dimensional harmonic oscillator energy representation of radial matrix element.

College Physics•Jan 1, 2013•0 citations

Application of radial basic operators of three-dimensional isotropic harmonic oscillator

Xiu-Lao Tian

By using radial basic operators, the recurrence relation of eiginfunctions, the matrix elements and expectation value of any function of operators are easily obtained.

College Physics•Jan 1, 2004•0 citations

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

Yao-Min Di

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.

Journal of Xuzhou Normal University•Jan 1, 2004•0 citations

Matrix elements in harmonic oscillator representations I. General solution and application to one dimension

Stephen G. Bell

General expressions have been obtained for the matrix elements of linear or radial perturbations in the representations of the one-, two-, and three-dimensional harmonic oscillators. The solutions are also general for the two types of matrix element where the two wave functions belong to the same basis set or to two different basis sets. In this paper these expressions are applied to one- dimensional problems.

Journal of Physics B Atomic and Molecular Physics•Jun 1, 1970•13 citations

GENERAL FORMULAS FOR RADIAL MATRIX ELEMENTS OF ISOTROPIC HARMONIC OSCILLATORS

Hou Chun-Feng, SUN XIU-DONG, Zhou Zhong-Xiang +2 more

The general formulas for radial matrix elements p|n′l′> and q|n′m′> of three-dimensional and two-dimensional isotropic harmonic oscillators are derived-

Acta Physica Sinica•Jan 1, 1999•13 citations

RECURRENCE FORMULA FOR RADIAL MATRIX ELEMENTS OF THREE-DIMENSIONAL ISOTROPIC HARMONIC OSCILLATOR

C Chen

The recurrence formula for radial matrix elements 〈 nl|r\+p|n′l′ 〉 of three\|dimensional isotropic harmonic oscillator are derived.

Acta Physica Sinica•Jan 1, 2000•0 citations
The matrix elements of powers of r 2 are evaluated in the basis of radial wavefunctions of a three-dimensional harmonic oscillator as a terminating type of generalised hypergeometric function 3 F 2 . They are employed to calculate the low-order moments of the radial density distribution. The form of radial density distribution for large values of oscillator quanta are given.