对于希尔伯特空间$\mathcal{F}$中稠密定义的自伴算子$\mathcal{H}$，算子$\exp(-it\mathcal{H})$是薛定谔方程$iψ'_t=\mathcal{H}ψ$的演化算子，即如果$ψ(0,x)=ψ_0(x)$，则$ψ(t,x)=(\exp(-it\mathcal{H})ψ_0)(x)$ for $x\in Q.$空间$\mathcal{F}$是定义在抽象空间$Q$上的波函数$ψ$的空间，量子系统的位形空间，$\mathcal{H}$是系统的哈密顿量。本文用自伴有界算子族$S(t), t\geq 0$表示$t$的所有实值的算子$\exp(-it\mathcal{H})$，该算子族与算子$-\mathcal{H}$相切.可以使用$S(t)=\exp(-t\mathcal{H})$，或者使用论文中列出的其他简单族$S$。主要定理是在$\mathcal{F}$中有界算子半群的水平上证明的，因此它的一般性使它的应用范围更广。提供了两个应用实例。
英文摘要：
For a densely defined self-adjoint operator $\mathcal{H}$ in Hilbert space $\mathcal{F}$ the operator $\exp(-it\mathcal{H})$ is the evolution operator for the Schrödinger equation $iψ'_t=\mathcal{H}ψ$, i.e. if $ψ(0,x)=ψ_0(x)$ then $ψ(t,x)=(\exp(-it\mathcal{H})ψ_0)(x)$ for $x\in Q.$ The space $\mathcal{F}$ here is the space of wave functions $ψ$ defined on an abstract space $Q$, the configuration space of a quantum system, and $\mathcal{H}$ is the Hamiltonian of the system. In this paper the operator $\exp(-it\mathcal{H})$ for all real values of $t$ is expressed in terms of the family of self-adjoint bounded operators $S(t), t\geq 0$, which is Chernoff-tangent to the operator $-\mathcal{H}$. One can take $S(t)=\exp(-t\mathcal{H})$, or use other, simple families $S$ that are listed in the paper. The main theorem is proven on the level of semigroups of bounded operators in $\mathcal{F}$ so it can be used in a wider context due to its generality. Two examples of application are provided.
On a relation of pseudoanalytic function theory to the two-dimensional stationary Schroedinger equation and Taylor series in formal powers for its solutions
