We consider the spectral problem for lattice Schrödinger operators with polynomial potentials. The eigenfunctions in the discrete spectrum of these operators correspond to the trigonometric moments of the periodic solutions of certain ordinary differential equations. Relying on this observation, the classical theory of moments permits the derivation of exact analytical and numerical bounds to the eigenvalues.

• Received 20 June 1988

DOI:https://doi.org/10.1103/PhysRevA.39.3256