Periodic Impurities in a Periodic Lattice

Because binary delta-function lattices of the Kronig-Penney type which have been previously studied are incapable of describing several important features of real crystals, the eigenvalue problem for a periodic linear chain ⋯A(BB⋯BB)A(BB⋯BB)⋯ of arbitrary square-well, A and B atoms of an arbitrary concentration is taken up and solved. The methods used are generalizable to other binary or multi-nary chains. It is shown that a theorem of Saxon and Hutner and of Luttinger relating to the preservation of the common forbidden energies of pure A and pure B lattices in a mixed A, B lattice is peculiar to their deltafunction representations of A and B, and is without general validity.