Laplace-Runge-Lenz vector for arbitrary spin
Mathematical Physics
2014-01-10 v3 math.MP
Quantum Physics
Abstract
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of Hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 are expressed via solutions of an ordinary differential equation of first order..
Cite
@article{arxiv.1308.4279,
title = {Laplace-Runge-Lenz vector for arbitrary spin},
author = {A. G. Nikitin},
journal= {arXiv preprint arXiv:1308.4279},
year = {2014}
}
Comments
This is a REVTEX form of the previous version with minor corrections