双变量厄米多项式递推关系与积分公式的简捷推导

A simple and neat approach to derive the recurrence relations and mathematical integral formulas of two-variable Hermite polynomial

基于正规乘积和反正规乘积性质与双变量厄米多项式的母函数形式,利用相干态表象完备性的高斯积分形式,系统而全面的导出双变量厄米多项式的算符恒等式、递推关系与积分公式,此推导方法简捷明了.

Based on the properties of normal （anti- normal） ordering product of quantum operators and Baker-Hausdorff operator equation, using the Gauss integral form of coherent state representation completeness, we derive some operator identities, recursive relations and integral formulas related to two- variable Hermite polynomial.Compared with other methods, this method is easier and heater in theory and application.