Open AccessBinomial theorem involving Hermite polynomials and negative-binomial theorem involving Laguerre polynomials
Author(s) -
Hong-Yi Fan,
Lou Sen-Yue,
Xiao-Yin Pan,
Cheng Da
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.240301
Subject(s) - laguerre polynomials , binomial theorem , hermite polynomials , classical orthogonal polynomials , mathematics , difference polynomials , orthogonal polynomials , generating function , negative binomial distribution , laguerre's method , binomial (polynomial) , operator (biology) , discrete orthogonal polynomials , polynomial , algebra over a field , discrete mathematics , pure mathematics , mathematical analysis , statistics , poisson distribution , biochemistry , chemistry , repressor , transcription factor , gene
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.