Problem: Density of States for Hybridized Bands

   If electrons can jump between a broad band [described by ] and a narrow energy level at , then the band structure exhibits signs of hybridization: A mixing of electronic states when the and energies are close (see Problem 5.2). In a simple model, the hybridized energy levels can be calculated as

Assume that the broad band has , a constant DOS over a bandwidth , and for or . For the narrow band the DOS peaks sharply at energy , but the total number of states is the same as in the broad band; . Calculate the DOS for the hybridized band.