1202.1321 (Isaac Shnaid)

Modified Schrödinger equation, its analysis and experimental
verification    [PDF]

Isaac Shnaid

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.

View original: http://arxiv.org/abs/1202.1321