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Journal of Southwest University

Integration Over Non-symmetric Projective Operators of the Coherent State

LI Ti-jun

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

This paper presents a new method for obtaining the integral of non-symmetric projective operators of the coherent state: the non-symmetric operator is first converted into symmetric by means of the eigenvalue equations of operator functions,and then the integral of the non-symmetric operator can be obtained by completeness relation of coherent states.Several examples are given to illustrate the use of this method.

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European Journal of Physics•Apr 8, 2020•1 citation
This paper presents a new method for obtaining the integral of non-symmetric projective operators of the coherent state: the non-symmetric operator is first converted into symmetric by means of the eigenvalue equations of operator functions,and then the integral of the non-symmetric operator can be obtained by completeness relation of coherent states.Several examples are given to illustrate the use of this method.
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
Abstract Operators play an important role in the formalism of quantum mechanics. By means of the technique of integration within an ordered product of operators and Dirac notation, we analytically prove that a new kind of asymmetric two-mode projection integral operator and another asymmetric two-mode Fock state projection summation operator are equal to the same Hermitian operator. For such Hermitian operator, we also rigorously demonstrate it corresponds to a parity measurement of a two-mode quantum state after passing through a beam splitter. The method used in this work provides a good exercise in quantum mechanics at the graduate level.