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International Journal of Theoretical Physics

New Operator Identities and Integration Formulas Regarding to Hermite Polynomials Obtained via the Operator Ordering Method

Hong-Yi Fan, Wang Tong-Tong

Published Aug 11, 2008• 10 citations
Publisher
DOI
10.1007/s10773-008-9819-6

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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.