Fluctuation effects in impurity band formation

A concept of “pseudo-wave number” is introduced to describe the nature of electronic states in disordered crystals. In one dimension, the formation of an impurity band is interpreted as a growth of a pole of localized mode due to one impurity to a finite, measurable, closed contour in the complex wave number plane. Several formulas about the density of states, the correlation functions, and the transition probabilities related to the localization problem are given. An improvement of the impurity band density-of-states which includes potential fluctuations due to pairing is obtained.