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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(sinx)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)≠V(x), and spell out the consequences for the form of the dispersion relation.
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