Derivation of the Schrodinger equation from the Hamilton-Jacobi equation in Feynman's path integral formulation of quantum mechanics

作者：Field J H^*

来源：European Journal of Physics, 2011, 32(1): 63-87.

DOI：10.1088/0143-0807/32/1/007

It is shown how the time-dependent Schrodinger 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. Schrodinger'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.

• 出版日期2011-1