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

Details The energy spectrum of complex periodic potentials of the Kronig-Penney type The energy spectrum of complex periodic potentials of the Kronig-Penney type

1999-09-20

arxiv.org/abs/cond-mat/9909294v1

Physics

Condensed Matter

4 pages, 2 figures

Scientific paper

10.1016/S0375-9601(99)00672-6

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 $V^*(x)\neq V(x)$, and spell out the consequences for the form of the dispersion relation.

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