The time-dependent Schrödinger equation revisited: Quantum optical and classical Maxwell routes to Schrödinger's wave equation

Abstract

In a previous paper [1-3] we presented quantum field theoretical and classical (Hamilton-Jacobi) routes to the time-dependent Schrödinger's equation (TDSE) in which the time t and position r are regarded as parameters, not operators. From this perspective, the time in quantum mechanics is argued as being the same as the time in Newtonian mechanics. We here provide a parallel argument, based on the photon wave function, showing that the time in quantum mechanics is the same as the time in Maxwell equations. © 2010 Springer-Verlag Berlin Heidelberg.