本文利用有序算符内的积分(IWOP)技术,构造了一个基于单变量厄米多项式H2jξ*+τξ2τ的新复变函数空间,该空间与纠缠态表象及施温格玻色环境下的自旋相干态有关。推导出了包含二元厄米多项式的二项式定理,有助于构造新的复变函数空间。同时还提出了一种新的基于H2jξ*+τξ2τ的积分变换及其逆变换,这对于推导某些算符恒等式是很有用的。

A new complex function space whose basis is the single-variable Hermite polynomial H2jξ*+τξ2τ is constructed,which is related to both entangled state representation and spin coherent state in Schwinger bosonic realization.New binomial theorem involving two-variable Hermite polynomial is derived,which helps to constitute the new complex function space.We also present a new integration transformation of the basis H2jξ*+τξ2τ with its reciprocal transformation which is useful to deriving some operator identities.