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Journal of Heze University

Deducing Function Space from the Comherent State and Entangled State Representation

Zhang Bing-yun

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Using the technique of integration within an ordered product of operators(IWOP),corresponding function space is deduced from the completeness of the coherent state and the entangled state.And the application of double variable Hermite polynomials is discussed.

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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.