New approach to generating functions of single- and two-variable even- and odd-Hermite polynomials and applications in quantum optics

Abstract

Using the IWOP technique and completeness of representation, we obtain the integral expressions of single- and two-variable Hermite polynomials. Based on this, we further derive the generating functions of single- and two-variable even- and odd-Hermit polynomials. This method seems more concise and direct. In addition, some applications such as deriving new formula and constructing new two-mode quantum states are discussed. It is found that two-variable Hermite polynomials excitation can used to produce entangled coherent states.