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- W2014163721 abstract "Associated Lamé potentials V(x)=a(a+1)msn2(x,m)+b(b+1)mcn2(x,m)/dn2(x,m) are used to construct complex, PT-invariant, periodic potentials using the anti-isospectral transformation x→ix+β, where β is any nonzero real number. These PT-invariant potentials are defined by VPT(x)≡−V(ix+β), and have a different real period from V(x). They are analytically solvable potentials with a finite number of band gaps, when a and b are integers. Explicit expressions for the band edges of some of these potentials are given. For the special case of the complex potential VPT(x)=−2msn2(ix+β,m), we also analytically obtain the dispersion relation. Additional new, solvable, complex, PT-invariant, periodic potentials are obtained by applying the techniques of supersymmetric quantum mechanics." @default.
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- W2014163721 date "2004-04-01" @default.
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- W2014163721 title "Analytically solvable PT-invariant periodic potentials" @default.
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- W2014163721 doi "https://doi.org/10.1016/j.physleta.2004.03.006" @default.
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