Nonrelativistic quantum particles on the Minkowski plane
Quantum Physics
2020-05-26 v4 Mathematical Physics
math.MP
Abstract
The quantum-mechanical problems of a nonrelativistic free particle, a harmonic oscillator and a Coulomb particle on Minkowski plane are discussed. The Schr\"odinger equations for eigenvalues are obtained using the Beltrami-Laplas operator of the pseudo-Euclidean plane and the corresponding potentials. It is shown that, in contrast to the standard problem on Euclidean plane, in addition to the continuous spectrum, a free particle has a discrete energy levels and a Coulomb particle, in addition to the discrete spectrum, has unstable states that describe the incidence of a particle on isotropic lines forming a metric cone.
Cite
@article{arxiv.2002.11990,
title = {Nonrelativistic quantum particles on the Minkowski plane},
author = {N. A. Gromov and I. V. Kostyakov and V. V. Kuratov},
journal= {arXiv preprint arXiv:2002.11990},
year = {2020}
}