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arXiv · 1202.1321

Modified Schrödinger equation, its analysis and experimental verification

Isaac Shnaid
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Abstract

According to classical non-relativistic Schrödinger equation, any local perturbation of wave function instantaneously affects all infinite region, because this equation is of parabolic type, and its solutions demonstrate infinite speed of perturbations propagation. From physical point of view, this feature of Schrödinger equation solutions is questionable. According to relativistic quantum mechanics, the perturbations propagate with speed of light. However when appropriate mathematical procedures are applied to Dirac relativistic quantum equation with finite speed of the wave function perturbations propagation, only classical Schrödinger equation predicting infinite speed of the wave function perturbations propagation is obtained. Thus, in non-relativistic quantum mechanics the problem persists. In my work modified non-relativistic Schrödinger equation is formulated. It is also of parabolic type, but its solutions predict finite speed of the wave function perturbations propagation. Properties of modified Schrödinger equation solutions are studied. I show that results of classical Davisson-Germer experiments with electron waves diffraction support developed theoretical concept of modified Schrödinger equation, and predict that speed of the wave function perturbations propagation has order of magnitude of speed of light.

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Isaac Shnaid. 2012-02-07. Modified Schrödinger equation, its analysis and experimental verification. https://arxiv.org/abs/1202.1321

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