Complex variables in quantum mechanics
Complex variables in quantum mechanics
复制标题
量子力学中的复变量
DOI：
10.1098/rspa.1937.0094
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发表时间：
1937
期刊：
影响因子：
--
通讯作者：
P. Dirac
中科院分区：
文献类型：
--
作者：
P. Dirac
量子力学的一般表示理论要求人们用一组实变量q 'r的函数来表示一个动力系统的状态，每一个实变量q 'r都有一个由离散点或连续点组成的域，或者两者都有。一个动态变量用两个实变量q ' r和q ' r的函数表示，形成一个广义的“矩阵”。在本文中，我们将证明，在某些情况下，根据复变函数理论，把我们的一些变量q ' r看作复变变量，并假定状态和动态变量的表示依赖于它们是有利的。在通常的理论中，s的定义域是某些可观测值q ' r的特征值。当我们把q看成复变量的时候，q的意义就会消失，但是，我们有，一些漂亮的数学特征出现了，我们获得了相当大的数学能力来计算特定的例子。
The general representation theory of quantum mechanics requires one to represent the states of a dynamical system by functions of a set of real variables q 'r, each of which has a domain consisting of either discrete points or a continuous range of points, or possibly both together. A dynamical variable is represented by a function of two such sets of real variables q ' r and q " r forming a generalized “matrix". In this paper we shall show that in certain cases it is advantageous to consider some of our variables q ' r as complex variables and to suppose the representatives of states and dynamical variables to depend on them in accordance with the theory of functions of a complex variable. In the usual theory the domains of the s are the eigenvalues of certain observables q " r . This significance of the q " s of course gets lost when we consider them as complex variables, but we have, however, some beautiful mathematical features appearing instead, and we gain a considerable amount of mathematical power for the working out of particular examples.