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

Simplified method of calculating matrix elements of operators for harmonic oscillator

Ju Guo-Xing

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Liang Junwu

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.

College Physics•Jan 1, 2009•0 citations

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

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

Unified Representation of Quantum Mechanics on One-dimensional Harmonic Oscillator

Yongqin Wang

A quantum state corresponds to a specific wave function. We adopt a new mathematical method [1] to improve Dirac's ladder operator method. A set of orthonormal wave functions will be used to associate the operator with the square matrix corresponding to it. These allow us to determine the matrix elements by using the operator relations without having to know the specific wave functions. As a result, we can get the direct results of matrix mechanics and wave mechanics on one-dimensional Harmonic oscillator and their descriptions will be also unified.

•Mar 7, 2013•1 citation

Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics ‐ quantum phase operator as a special case

M. Davidović

Abstract Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the |n〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.

Fortschritte der Physik•Feb 26, 2003•5 citations

Diabatic Hamiltonian matrix elements made simple

K. Hagino, G. F. Bertsch

With a view to applying the generator coordinate method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. The method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

arXiv:2201.04495•Physical Review C•Mar 22, 2022•6 citations
A quantum state corresponds to a specific wave function. We adopt a new mathematical method [1] to improve Dirac's ladder operator method. A set of orthonormal wave functions will be used to associate the operator with the square matrix corresponding to it. These allow us to determine the matrix elements by using the operator relations without having to know the specific wave functions. As a result, we can get the direct results of matrix mechanics and wave mechanics on one-dimensional Harmonic oscillator and their descriptions will be also unified.
Abstract Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the |n〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.