THE SPECTRA OF THE SCHROEDINGER OPERATOR

Abstract

We look at the Schrodinger operator H=-(DELTA)+q(x) where (DELTA) is the Laplacian and q(x)(epsilon)R('n). We give sufficient conditions for the spectrum of H to contain the interval of the form {lcub}a,(INFIN)) and sufficient conditions for the essential spectrum of H to contain the interval of the form {lcub}b,(INFIN)). Our estimates for the lower bounds of a and b are positive numbers. We allow q(x) to be negative in some region. Our results are in R('2) and in R('n).