Structure of the spectrum of a bloch electron in a magnetic field in a two-dimensional lattice

A study is made of the Hamiltonian H of an electron in a two-dimensional lattice of point potentials in a transverse magnetic field whose flux is rational. An expansion of H in a direct integral over a two-dimensional torus of the reciprocal lattice of operators described by finite-dimensional matrices is obtained. This expansion is used to investigate the structure of the spectrum of H, whose continuum eigenfunctions are found.