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

doi:10.1088/1674-1056/22/6/060301

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/22/6/060301

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

袁洪春^a, 李恒梅^b, 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

收稿日期:2012-10-14 修回日期:2012-12-18 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
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).

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

Received:2012-10-14 Revised:2012-12-18 Online:2013-05-01 Published:2013-05-01
Contact: Yuan Hong-Chun E-mail:yuanhch@126.com, yuanhc@czu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: two-variable Hermite polynomial, entangled state representation, operator identities

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.

Key words: two-variable Hermite polynomial, entangled state representation, operator identities

中图分类号: (Quantum mechanics)

03.65.-w

42.50.-p (Quantum optics)

袁洪春, 李恒梅, 许雪芬. New operator identities regarding to two-variable Hermite polynomial by virtue of entangled state representation[J]. 中国物理B, 2013, 22(6): 60301-060301.

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[J]. Chin. Phys. B, 2013, 22(6): 60301-060301.

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

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

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