The Time-Dependent Schrödinger Equation Revisited: Quantum Optical and Classical Maxwell Routes to Schrödinger’s Wave Equation
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.
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I would like to thank R. Arnowitt, C. Summerfield, and S. Weinberg for useful and stimulating discussions. This work was supported by the Robert A. Welch Foundation grant number A-126 and the ONR award number N00014-07-1-1084.
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