The Hydrogen Atom and the Equivalent Form of Levy-Leblond Equation
Quantum Physics
2017-05-30 v4 Materials Science
Abstract
We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation. Furthermore, we analyze the case with four dimensional matrices and propose a Hamiltonian for the equation in (3+1) dimensions and solve it for a Coulomb potential. We show that the quantized energy levels for the hydrogen atom are obtained and the result is consistent with non-relativistic quantum mechanics.
Keywords
Cite
@article{arxiv.1607.06729,
title = {The Hydrogen Atom and the Equivalent Form of Levy-Leblond Equation},
author = {Muhammad Adeel Ajaib},
journal= {arXiv preprint arXiv:1607.06729},
year = {2017}
}
Comments
10 pages, Accepted by Chinese Physics Letters