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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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S03759...
Related URL: http://dx.doi.org/10.1016/j.physleta.2004.03.006
Abstract
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 |
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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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