Investigations On The Bivariate Hermite Polynomials In Quantum Optics

Bivariate Hermite polynomials,which is a special function,has been widely used in quantum optics theory.In this dissertation,we discuss Bivariate Hermite polynomials in seven chapters.In introduction,we emphasize that Bivariate Hermite polynomials is a special funtion with clearly physical meanings.In chapter 2,based on the Gauss integral form of coherent state representation completeness we draw out Bivariate Hermite polynomials;and in chapter 3,by using IWOP method,we derive some operator identities and integral formulas related to Bivariate Hermite polynomials.In chapter 4,we discuss Bivariate Hermite polynomials in entangled state representation;we introduce Hermite polynomials and the relationship between Hermite polynomials and Bivariate Hermite polynomials in chapter 5,and the use of Bivariate Hermite polynomials in chapter 6.Conclusions are summarized in chapter 7.