Binomial theorems related to two-variable Hermite polynomials and its application in quantum optics
Fan Hong-Yi, Lou Sen‐Yue, Xiao‐Yin Pan, Da Cheng · Acta Physica Sinica · 2014
We propose an operator Hermite polynomial method, namely, to replace the special functions' argument by quantum mechanical operator, and in this way we have derived two binomial theorems related to two-variable Hermite polynomials. This method is concise and may be of help in deducing many operator identities, which may become a new branch in mathematical physics theory.