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Communications in Theoretical Physics

New Form of Legendre Polynomials Obtained by Virtue of Excited Squeezed State and IWOP Technique in Quantum Optics

Fan Hong‐Yi, Meng Xiang-Guo, Ji‐Suo Wang

Published Nov 1, 2006• 24 citations
Publisher

Abstract

Using the technique of integration within an ordered product of operators and the intermediate coordinate-momentum representation in quantum optics, as well as the excited squeezed state we derive a new form of Legendre polynomials.
DOI
10.1088/0253-6102/46/5/015

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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.
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Via the route of developing Dirac's symbolic method by virtue of the technique of integration within an ordered product (IWOP) of operators we derive various entangled state representations, squeezed states, and operator ordering formulae. We show how the entangled states can be applied to many aspects of quantum optics theory. The applications of the entangled states in the interdisciplinary study of quantum optics and Fourier optics are also introduced. All these discussions exhibit the power of Dirac's symbolic method with the aid of the IWOP technique.