ON SMALL PERTURBATIONS OF THE SCHRODINGER OPERATOR WITH A PERIODIC POTENTIAL

Consideration is given to small perturbations of a potential, periodic with respect to the variables x(j), j = 1, 2, 3, by a function period ic in x(1) and x(2) that decays exponentially as \x(3)\ --> infinity. It is shown that in the neighborhood of energies corresponding to the extrema in the third quasimomentum component of nondegenerate eigenval ues of the Schrodinger operator, with the periodic potential considere d in a cell, there exists a unique solution (up to within a numerical factor) to the integral equation describing both the eigenvalues and r esonance levels. The asymptotic behavior of the eigenvalues and resona nce levels is investigated.