Entangled state representation for deriving new operator identities regarding to two-variable Hermite polynomial

TL;DR

This paper uses entangled state representation and IWOP technique to derive new operator identities and generating functions for two-variable Hermite polynomials, aiding quantum optical calculations.

Contribution

It introduces a novel method combining entangled state representation and IWOP to derive new identities and generating functions for TVHPs.

Findings

New operator identities for TVHP derived

New generating function formulas for TVHP established

Method allows derivation of integration formulas without explicit integration

Abstract

In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.