Intermediate Hamiltonian and lower bounds to localised energy levels

Abstract

The intermediate Hamiltonian method is applied to the calculation of lower bounds to localised energy levels due to impurities in solids. This technique, together with judicious application of the Koster-Slater method, giving upper bounds in favourable cases, allows the exact localised energy levels to be bracketed. An application to a one-dimensional Kronig-Penney potential with rectangular impurities is presented. The accuracy attained varies in the range of 2.43% of the deviation of the energy level from its band of origin.