The Modified Quantum Mechanics from the Covariant Generalized Uncertainty Principle
General Physics
2020-10-07 v1
Abstract
One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we consider a covariant version of the generalized uncertainty principle to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy-momentum dispersion relation is modified. Starting with the modified dispersion relation, the corrections to the wave function are obtained and the problems of the particle in a box and the Hydrogen atom are revisited.
Cite
@article{arxiv.2010.02702,
title = {The Modified Quantum Mechanics from the Covariant Generalized Uncertainty Principle},
author = {M. Seifi and A. S. Sefiedgar},
journal= {arXiv preprint arXiv:2010.02702},
year = {2020}
}