GENERALIZED BETHE-ANSATZ EQUATIONS FOR HOFSTADTER PROBLEM

The problem of diagonalization of the quantum mechanical Hamiltonian, governing dynamics of an electron on a two-dimensional triangular or s quare lattice in external uniform magnetic field, applied perpendicula rly to the lattice plane, the flux through lattice cell, divided by th e elementary quantum flux, being a rational number, is reduced to the generalized Bethe ansatz like equations on the high genus algebraic cu rve. Our formulae for the trigonometric case, where the genus of the c urve vanishes, contain as a particular case a recent result of Wiegman n and Zabrodin.