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Communications in Theoretical Physics

Solution to Operator Fredholm Equation in Bipartite Entangled State Representation and Its Applications

Fan Hong‐Yi, Ji‐Suo Wang

Published Apr 1, 2007• 4 citations
Publisher

Abstract

Based on the bipartite entangled state representation and using the technique of integration within an ordered product (IWOP) of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials.

DOI
10.1088/0253-6102/47/4/008

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Based on the bipartite entangled state representation and using the technique of integration within an ordered product (IWOP) of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and 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.