本文从量子光学的方法来引出双变量厄密多项式, 即用Fock空间中光子的产生算符和消灭算符不对易性,［a,a*］=1,说明双变量厄密多项式的来源并用它简捷明了地表述若干基本算符的排序恒等式。我们用有序算符内的积分理论(IWOP技术)讨论双变量厄密多项式的正交性和完备性,并指出双模厄密多项式在求正规乘积算符的P-表示中的应用。

We introduce the bivariate Hermite polynomials Hmn on quantum optics theory,using ［a,a*］=1.We explain the origin of Hmn and derive some operator identities involving Hmn. By virtue of the IWOP method we prove the orthogonal and completeness of Hmn, and using Hmn we derive the P-representation of normal ordered operators.