Scattering theory of defects in crystals

Abstract

The theory of scattering is applied here to the problem of the electronic states of impurities. The S, T and K matrices, the Lippman-Schwinger and Dyson equations are used to formulate the problem. The standard concepts, methods and results of scattering theory applied to impurities discussed include the scattering amplitude, the Fredholm determinant, dispersion relations, Regge poles, Levinson's theorem and Fadeev's equations. Physical consequences considered are the change in density of states, eigenstates and transport theory. The necessity of extending the scattering formalism to many-body theory is discussed. The relation between scattering theory and other methods of impurity theory is also mentioned.