The energy spectrum of complex periodic potentials of the Kronig–Penney type

Abstract

We consider a complex periodic PT-symmetric potential of the Kronig–Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form V= i(sin x) 2 N+1 , and in particular the absence of anti-periodic solutions. In this model we show explicitly why these solutions disappear as soon as V ∗(x)≠V(x) , and spell out the consequences for the form of the dispersion relation.