The quantum mechanics based on a general kinetic energy
Abstract
In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy operator include the standard Schrodinger equation, the relativistic Schrodinger equation, the fractional Schrodinger equation, the Dirac equation, and the deformed Schrodinger equation. We reveal that the Klein-Gordon equation has a hidden non-Hermitian kinetic energy operator. The probability continuity equation with sources indicates that there exists a different way of probability transportation, which is probability teleportation. An average formula is deducted from the relativistic Schrodinger equation, the Dirac equation, and the K-G equation.
Keywords
Cite
@article{arxiv.1602.05844,
title = {The quantum mechanics based on a general kinetic energy},
author = {Yuchuan Wei},
journal= {arXiv preprint arXiv:1602.05844},
year = {2016}
}
Comments
This paper was published with one page missing and some typos, but the journal does not want to correct. I have to post the full version here