A general method for computing the spectra of periodic Schrödinger operators is introduced here. The method is based on the classical theory of moments, and provides exact, rapidly converging bounds to the energy bands of periodic Hamiltonian operators, in any number of space dimensions. As an illustration of the general theory, we develop an application to the electronic states of modulated superlattices, in the envelope-function approximation. This allows one to obtain important information on the effects of variable effective mass and relative-band-offset ratio in these materials.

• Received 13 September 1991

DOI:https://doi.org/10.1103/PhysRevB.46.7037