  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.
