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 $V=i(\sin x{)}^{2N+1}$, and in particular the absence of anti-periodic solutions. In this model we show explicitly why these solutions disappear as soon as $V^{\ast }(x)\ne V(x)$, and spell out the consequences for the form of the dispersion relation.

4 pages, 2 figures

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