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

College Physics

Calculation of matrix elements of coordinate operator of harmonic oscillator with integer power by coherent state functions

Liang Junwu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Matrix elements of coordinate operator with integer power in the bases of harmonic oscillator are derived by using the properties of coherent state functions.The method used in this paper has its merit in comparison with other documents.

Related papers

Coherent State Calculation of Coordinate Operator Matrix Element of Harmonic Oscillator

Xuehua Jiang

Matrix element of coordinate operator ~l of harmonic oscillator is discussed by using coherent state and normal product.The general formula calculating matrix element of ~l is obtained.That is the same to that of the document [1-2]. This offers a new method for dealing with the perturbation of harmonic oscillator.

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

Simplified method of calculating matrix elements of operators for harmonic oscillator

Ju Guo-Xing

The problems of simply and directly computing the matrix elements of coordinate operator for the harmonic oscillator in both the number states and the coherent states representations are studied in detail,the explicit procedures are given and some issues related to the methods and procedures in the literatures are commented.

College Physics•Jan 1, 2011•0 citations

Matrix elements of x N and p N for the quantum oscillator

Srilal Muditha Weerasinghe, H. W. Graben

General formulas for the linear oscillator matrix elements of positive integer powers of the position coordinate and the momentum coordinate are derived.

European Journal of Physics•Sep 1, 1994•1 citation

Hydrogen atom in the four-dimensional oscillator representation: matrix elements of zn

Hilda A. Cerdeira

The authors presents a calculation of the matrix elements of z n between four-dimensional harmonic oscillator states. It is shown that a knowledge of the scalar product of two harmonic oscillator states of different frequencies is enough to generate the matrix elements of any power of z. These can be found by taking appropriate derivatives of the aforementioned scalar product.

Journal of Physics A Mathematical and General•Oct 1, 1985•8 citations

A concise approach to derivation of the general formula of matrix element 〈n|(f■+g■)~k|m〉 for harmonic oscillator

Heng-Mei Li

Based on the normally ordered form of operat or(f■+g■)k,the general formula of its matrix element for harmonic oscillator is deduced compactly by virtue of the relation between un-normalized coherent state and harmonic oscillator's eigenstate,and the result is also discussed.It is clear that this adopted method is very simply and concise.

College Physics•Jan 1, 2011•0 citations

Multidimensional harmonic oscillator matrix elements

Francisco Marcelo Fernández, Richard H. Tipping

Multidimensional harmonic oscillator matrix elements of arbitrary products of exponentials for operators containing only linear and quadratic terms in the creation and annihilation operators are obtained. A simple and straightforward method is presented that leads to recurrence relations and generating functions for such matrix elements. Results are shown to be general enough to cover the cases of Franck–Condon overlaps, transition probabilities for time-dependent harmonic oscillators, and correlation functions for electronic spectra.

The Journal of Chemical Physics•Nov 1, 1989•6 citations
Multidimensional harmonic oscillator matrix elements of arbitrary products of exponentials for operators containing only linear and quadratic terms in the creation and annihilation operators are obtained. A simple and straightforward method is presented that leads to recurrence relations and generating functions for such matrix elements. Results are shown to be general enough to cover the cases of Franck–Condon overlaps, transition probabilities for time-dependent harmonic oscillators, and correlation functions for electronic spectra.