Perturbation theory formulas for the Schrödinger equation with a nonsmooth periodic potential

Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schrödinger operator in $R^3$. An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.