Quantum harmonic analysis on phase space
Quantum harmonic analysis on phase space
复制标题
相空间的量子调和分析
DOI：
10.1063/1.526310
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发表时间：
1984
影响因子：
1.3
通讯作者：
R. Werner
中科院分区：
文献类型：
--
作者：
R. Werner
相对于正则对易关系的不可约表示，定义了量子力学算符之间以及函数与算符之间的卷积，通常的Weyl变换充当傅立叶变换。这些运算的基本性质是在与R2n上的调和分析非常相似的情况下展开的。利用维纳近似定理的量子版本，建立了经典观测和量子观测的闭合相空间平移不变子空间之间的自然一一对应关系。
Relative to an irreducible representation of the canonical commutation relations, convolutions between quantum mechanical operators and between functions and operators are defined, for which the usual Weyl transform acts as a Fourier transform. Basic properties of these operations are developed in close analogy to harmonic analysis on R2n. Using the quantum version of Wiener’s approximation theorem, a natural one‐to‐one correspondence between the closed, phase‐space translation invariant subspaces of classical and quantum observables is established.