Periodic Schrödinger operators on a manifold.(English)Zbl 0655.58033

The present paper treats some spectral properties of the Schrödinger operator $$-\Delta +q$$ defined on an open Riemannian manifold with an isometry group $$\Gamma$$ whose orbit space is compact, where the function q is supposed to be periodic under the $$\Gamma$$-action. A generalization of the Bloch’s theorem is discussed. Examples of manifolds on which the Schrödinger operators have eigenvalues are exhibited.
Reviewer: T.Kobayashi

MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 35J10 Schrödinger operator, Schrödinger equation
Full Text: