The ground state energy of a charged particle on a Riemann surface
High Energy Physics - Theory
2010-12-20 v2 Mathematical Physics
math.MP
Abstract
It is shown that the quantum ground state energy of particle of mass m and electric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E_0=eB/2m. Remarkably, this formula is completely independent of both the geometry and topology of the Riemann surface. The formula is obtained by reinterpreting the quantum Hamiltonian as the second variation operator of an associated classical variational problem.
Keywords
Cite
@article{arxiv.1012.3337,
title = {The ground state energy of a charged particle on a Riemann surface},
author = {J. M. Speight},
journal= {arXiv preprint arXiv:1012.3337},
year = {2010}
}
Comments
5 pages, minor improvements and references added