Binomial theorem involving Hermite polynomials and negative-binomial theorem involving Laguerre polynomials

Author:

Fan Hong-Yi ,Lou Sen-Yue ,Pan Xiao-Yin ,Da Cheng , ,

Abstract

We propose an operator Hermite polynomial method, namely, we replace the arguments of the special function by quantum mechanical operators, and in this way we derive a binomial theorem involving Hermite polynomials and a negative-binomial theorem involving Laguerre polynomials. These two theorems will have essential applications in quantum optics calculations. This method is concise and helpful in deducing many operator identities, which may become a new branch in mathematical physics theory.

Publisher

Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences

Subject

General Physics and Astronomy

Reference14 articles.

1. Fan H Y, Ruan T N 1985 Commun. Theor. Phys. 4 181

2. Fan H Y, Ruan T N 1989 Commun. Theor. Phys. 12 219

3. Fan H Y 2012 Representation and Transformation Theory in Quantum Mechanics-Progress of Dirac’s Symbolic Method (2nd Ed.) (Hefei: University of Science and Technology of China Press) (in Chinese) [范洪义 2012 量子力学表象与变换论——狄拉克符号法进展 (合肥: 中国科学技术大学出版社)]

4. Fan H Y, Hu L Y 2010 Optical Transformation-From Quantum to Classical (Shanghai: Shanghai Jiao Tong University Press) (in Chinese) [范洪义, 胡利云 2010 光学变换——从量子到经典 (上海: 上海交通大学出版社)]

5. Fan H Y, Li X C 2012 Acta Phys. Sin. 61 200301 (in Chinese) [范洪义, 李学超 2012 物理学报 61 200301]

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