On the Quantization of a Theory Arising from a Variational Principle for Multiple Integrals with Application to Born's Electrodynamics
On the Quantization of a Theory Arising from a Variational Principle for Multiple Integrals with Application to Born's Electrodynamics
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论多重积分变分原理产生的理论的量子化及其在玻恩电动力学中的应用
DOI：
10.1098/rspa.1936.0143
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发表时间：
1936
期刊：
影响因子：
--
通讯作者：
P. Weiss
中科院分区：
文献类型：
--
作者：
P. Weiss
从经典力学到量子力学的过渡已经以各种方式表述。但所有这些方法都有一个共同的特点，那就是它们不是以牛顿力学的形式，而是以拉格朗日和汉密尔顿给出的形式作为出发点。这种形式的本质在于这样一个事实，即微分方程表示为一个变量，时间的v函数，广义坐标的变分原理的欧拉方程。因此，在其纯数学方面，量子化方法可以被看作是一种模式，它采用了由多个因变量和一个自变量的变分原理产生的某些概念和某些关系，并赋予它们新的含义。
The transition from classical mechanics to quantum mechanics has been formulated in various ways. But all these ways have the common feature that they use as starting point mechanics not in its Newtonian form, but in the form which it was given by Lagrange and Hamilton. The essence of this form consists in the fact that the differential equations are represented as Euler equations of a variational principle for v functions, the generalized coordinates, of one variable, the time. In its purely mathematical aspect the quantization method may, therefore, be regarded as a mode of taking certain notions and certain relations arising from a variational principle for several dependent and one independent variable and of giving them a new meaning.