Description of the spectral bands for some 2D periodic Schrödinger operators

摘要

In this paper, we are concerned with the study of the spectrum of operators with periodic potentials in 1D and 2D, modelling the interactions of an electron with regular lattices of ions. The classical Bloch theory asserts that the spectrum has a band structure and we are able to localize the spectral bands which are in the range of the potential and to prove estimates on their widths in the semiclassical limit.