Strict bounds for out-of-band frequencies due to impurities and defects in solids

Abstract

A method is described for the determination of strict upper and lower bounds on the frequencies of local modes due to impurities and defects in solids. The physical basis for the method stems from the dynamical properties of a small `defect region' in the solid which surrounds the defect or impurity of interest; mathematically, the method depends upon theorems due, in their original form, to Kato. The method does not depend for its use upon the availability of tabulated data.