Abstract
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 $\ensuremath{\cdots}A(BB\ensuremath{\cdots}BB)A(BB\ensuremath{\cdots}BB)\ensuremath{\cdots}$ 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.
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