The ground state energy of a charged particle on a Riemann surface

2010/12/15 by Martin Speight, J. M. Speight, Speight, J. M.
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1012.3337

5 pages, minor improvements and references added

arxiv created 2010/12/17 · arxiv updated 2010/12/20

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 E₀=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.

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