New operator identities regarding to two-variable Hermite polynomial by virtue of entangled state representation

Yuan Hong-Chun (袁洪春)^{a}, Li Heng-Mei (李恒梅)^{b}, Xu Xue-Fen (许雪芬)^{c}

a College of Optoelectronic Engineering, Changzhou Institute of Technology, Changzhou 213002, China; b School of Science, Changzhou Institute of Technology, Changzhou 213002, China; c School of Mathematics and Physics, Jiangsu Teachers University of Technology, Changzhou 213001, China

Abstract 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.

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11174114), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJD140001), and the Research Foundation of Changzhou Institute of Technology of China (Grant No. YN1106).

Yuan Hong-Chun (袁洪春), Li Heng-Mei (李恒梅), Xu Xue-Fen (许雪芬) New operator identities regarding to two-variable Hermite polynomial by virtue of entangled state representation 2013 Chin. Phys. B 22 060301

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