The authors prove a number of results asserting the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H), where H=-Δ+V and V and W are bounded. The existence of these eigenvalues is an important element in the theory of the colour of crystals. The basic theorems are proved in ℝv; stronger results for v=1 are also presented.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics