Analytic criteria in the qualitative spectral analysis of the Schroedinger operator

Abstract

A number of topics in the qualitative spectral analysis of the Schrödinger operator $-Δ+ V$ are surveyed. In particular, some old and new results concerning the positivity and semiboundedness of this operator as well as the structure of different parts of its spectrum are considered. The attention is focused on conditions both necessary and sufficient, as well as on their sharp corollaries.