The Elimination of the Nodes in Quantum Mechanics
The Elimination of the Nodes in Quantum Mechanics
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量子力学中节点的消除
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通讯作者：
P. Dirac
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作者：
P. Dirac
经典力学定律在应用于原子系统时必须进行概括，概括为应用于动力学变量的乘法交换律将被某些量子条件所取代，当给定 x 和 y 时，这些条件足以使人能够计算 xy - yx。由此可见，动力学变量不能是用十进制表示的普通数（这些数将被称为 c 数），但可以被认为是特殊类型的数（将被称为 q 数），其性质无法精确指定，但可以以与相应经典变量的使用方式非常相似的方式用于动力学问题的代数解。给动力学变量命名的唯一理由在于与经典理论的类比，例如。 g。 ，如果说 x、y、z 是电子的笛卡尔坐标，则仅意味着 x、y、z 是 q 数，它们以与经典解中电子的笛卡尔坐标类似的方式出现在问题的量子解中。可能会发生两个或多个 q 数类似于同一个经典量（当然，这种类比是不完美的，并且对于不同的 q 数而言在不同方面），因此具有相同的名称。例如，当人们考虑什么 q 数应被称为多重周期系统的频率时，就会发生这种情况，其中有轨道频率和过渡频率，其中任何一个在某些方面都对应于经典频率。在这种情况下，我们必须决定经典变量的哪些属性在动态上是最重要的，并且必须选择具有这些属性的 q 数作为相应的量子变量。
The laws of classical mechanics must be generalised when applied to atomic systems, the generalisation being that the commutative law of multiplication, as applied to dynamical variables, is to be replaced by certain quantum conditions, which are just sufficient to enable one to evaluate xy - yx when x and y are given. It follows that the dynamical variables cannot be ordinary numbers expressible in the decimal notation (which numbers will be called c-numbers), but may be considered to be numbers of a special kind (which will be called q-numbers), whose nature cannot be exactly specified, but which can be used in the algebraic solution of a dynamical problem in a manner closely analogous to the way the corresponding classical variables are used. The only justification for the names given to dynamical variables lies in the analogy to the classical theory, e. g. , if one says that x, y, z are the Cartesian co-ordinates of an electron, one means only that x, y, z are q-numbers which appear in the quantum solution of the problem in an analogous way to the Cartesian co-ordinates of the electron in the classical solution. It may happen that two or more q-numbers are analogous to the same classical quantity (the analogy being, of course, imperfect and in different respects for the different q-numbers), and thus have claims to the same name. This occurs, for instance, when one considers what q-numbers shall be called the frequencies of a multiply periodic system, there being orbital frequencies and transition frequencies, either of which correspond in certain respects to the classical frequencies. In such a case one must decide which of the properties of the classical variable are dynamically the most important, and must choose the q-number which has these properties to be the corresponding quantum variable.