College Physics

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

Heng-Mei Li

Published Jan 1, 2011• 0 citations

Abstract

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.

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 UniversityJan 1, 20040 citations

Matrix elements of X xk and e αX x k in the harmonic oscillator basis

Włodzisław Duch

General and compact formulae for matrix elements of x k and X k X k e αX are derived using the second quantisation technique.

Journal of Physics A Mathematical and GeneralDec 21, 198315 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 PhysicsJan 1, 20110 citations

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 PhysicsJan 1, 20090 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 SinicaJan 1, 199913 citations

Some New Quantum Operator Formulas—New Applications of the Coherent State

Fan Hong‐Yi, Ruan Tu-Nan

We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also

Communications in Theoretical PhysicsJul 1, 198310 citations