Spectral Theory of the Schroedinger Operators on Non-Compact Manifolds:211 Qualitative Results

摘要

The paper contains an expanded version of the authors' lectures in the Edinburgh211u001eschool on Spectral Theory and Geometry (Spring 1998). The authors tried to make 211u001ethe exposition as self-contained as possible. The main object of this paper is a 211u001eSchrodinger operator H = -(delta) + V(x) on a noncompact Riemannian manifold M. 211u001eThe author discusses two basic questions of the spectral theory for such 211u001eoperators: conditions of the essential self-adjointness (or quantum 211u001ecompleteness), and conditions for the discreteness of the spectrum in terms of 211u001ethe potential V.