Analytically solvable PT-invariant periodic potentials

Khare, Avinash ; Sukhatme, Uday (2004) Analytically solvable PT-invariant periodic potentials Physics Letters A, 324 (5-6). pp. 406-414. ISSN 0375-9601

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Associated Lame 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:PT-invariant Potentials; Supersymmetry
ID Code:17699
Deposited On:16 Nov 2010 12:50
Last Modified:17 May 2016 02:18

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