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Journal of Physics A Mathematical and General

Weyl correspondence and P-representation as operator Fredholm equations and their solutions

Hong-Yi Fan, John R. Klauder

Published Aug 9, 2006• 4 citations
Publisher

Abstract

Using the technique of integration within an ordered product of operators we construct operator Fredholm equations, which can help us to re-formulize the Weyl correspondence and P-representation. We then search for their solutions which present new formulae for deriving quantum operators' Weyl classical correspondence and P-representation. As the application, we deduce some new relations about the two-variable Hermite polynomials.

DOI
10.1088/0305-4470/39/34/016

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Using the technique of integration within an ordered product of operators we construct operator Fredholm equations, which can help us to re-formulize the Weyl correspondence and P-representation. We then search for their solutions which present new formulae for deriving quantum operators' Weyl classical correspondence and P-representation. As the application, we deduce some new relations about the two-variable Hermite polynomials.
By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.