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

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.