从量子力学费曼路径积分公式中的Hamilton-Jacobi方程导出薛定谔方程
Derivation of the Schrödinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics
摘要：
从经典力学的Hamilton-Jacobi方程和量子力学的Feynman路径积分公式的动力学假设出发，导出了含时的薛定谔方程.薛定谔自己出版的推导量子波动方程，其中第一个也是基于汉密尔顿-雅可比方程，也审查。时间相关方程的推导基于与费曼动力学假设等价的{ \it先验}假设。德布罗意的概念“物质波”和他们的相和群速度也进行了严格的讨论。
英文摘要：
It is shown how the time-dependent Schrödinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrödinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi equation, are also reviewed. The derivation of the time-dependent equation is based on an {\it a priori} assumption equivalent to Feynman's dynamical postulate. De Broglie's concepts of 'matter waves' and their phase and group velocities are also critically discussed.
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