Modified Schr\"odinger equation, its analysis and experimental verification

TL;DR

This paper proposes a modified Schr"odinger equation that predicts finite speed of wave function perturbations, aligning non-relativistic quantum mechanics with relativistic principles and supported by electron diffraction experiments.

Contribution

It introduces a new form of the Schr"odinger equation that incorporates finite propagation speed, addressing a fundamental inconsistency in traditional quantum mechanics.

Findings

Modified Schr"odinger equation predicts propagation speed close to the speed of light.

Experimental data from electron diffraction supports the finite speed hypothesis.

Theoretical analysis aligns with relativistic quantum mechanics principles.

Abstract

According to classical non-relativistic Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger equation is formulated. It is also of parabolic type, but its solutions predict finite speed of the wave function perturbations propagation. Properties of modified Schr\"odinger equation solutions are studied. I show that results of classical Davisson-Germer experiments with electron waves diffraction support developed theoretical concept of modified Schr\"odinger equation, and predict that speed of the wave function perturbations propagation has order of magnitude of speed of light.