一种推导厄米多项式的递推关系的方法

A New Approach to Deducing the Recurrence Relation of Hermite Polynomial

文章利用厄米多项式的母函数以及Baker-Hausdorf公式,推导出以动量算符为参变量的厄米多项式的正规乘积形式,基于此形式很容易导出有关厄米多项式的一些关系式。

By using the generating function of Hermite polynomial and Baker-Haussdorf operator formula,Hermite polynomial parameterized by the momentum operator is expressed as the normally ordered form,which is very easy to derive some well-known recurrence relations on Hermite polynomial.