Weyl Transformation and the Classical Limit of Quantum Mechanics
Weyl Transformation and the Classical Limit of Quantum Mechanics
复制标题
韦尔变换与量子力学的经典极限
DOI：
10.1063/1.1664478
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发表时间：
1968
影响因子：
1.3
通讯作者：
B. Leaf
中科院分区：
文献类型：
--
作者：
B. Leaf
从经典坐标和动量的函数得到量子算符的外尔对应是不正确的。为了计算量子力学的期望值作为维格纳密度函数的相空间平均值，不能使用经典函数，而必须使用外尔变换。这些变换的定义和它们的性质来自量子力学。它们的性质用一个厄密算子Δ（Q，K）表示，其Weyl变换是δ函数.维格纳函数是密度算符的变换。每一个Weyl变换都表现为两个在相谱上非负的函数的差。外尔变换不服从经典函数的代数。在经典极限ε → 0，Weyl变换成为经典函数，维格纳函数成为非负的整个相空间，和希尔伯特空间是由一组正交的向量，这是同时特征的交换坐标和动量Ope。
The Weyl correspondence for obtaining quantum operators from functions of classical coordinates and momenta is known to be incorrect. To calculate quantum‐mechanical expectation values as phase‐space averages with the Wigner density function, one cannot use classical functions but must use Weyl transforms. These transforms are defined and their properties derived from quantum mechanics. Their properties are expressed in terms of a Hermitian operator Δ(Q, K) whose Weyl transform is a δ function. The Wigner function is the transform of the density operator. Every Weyl transform is exhibited as a difference of two functions which are nonnegative on the phase spece. Weyl transforms do not obey the algebra of classical functions. In the classical limit ℏ → 0, Weyl transforms become classical functions, the Wigner function becomes nonnegative throughout the phase space, and the Hilbert space is spanned by an orthonormal set of vectors which are simultaneous eigenkets of the commuting coordinate and momentum ope...