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Derivation of the Schrödinger equation from the Hamilton-Jacobi equation in Feynman’s path integral formulation of quantum mechanics
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. Schr¨odinger’s own published derivations of quantum wave equations, the firs...
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. Schr¨odinger’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 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.
