On the Spectrum of Schrödinger Operators at the Half Space with a Certain Class of Boundary Conditions

Abstract

The spectrum of free Schrödinger operators at the half space with boundary condition ${\phi }_n–Q\phi =0$ ($\phi$ being the normal derivative, $Q$ a self-adjoint operator at the boundary) is investigated and a connection between its negative part and the spectrum of a family of Klein–Gordon type operators is stated.