A QES band-structure problem in one dimension

Khare, Avinash (2001) A QES band-structure problem in one dimension Physics Letters A, 288 (2). pp. 69-72. ISSN 0375-9601

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S03759...

Related URL: http://dx.doi.org/10.1016/S0375-9601(01)00527-8

Abstract

I show that the potential V(x,m) = [ b2/4 - m(1-m)a(a+1) ] sn2(x,m)/ dn2(x,m) - b ( a + ½ ) cn(x,m)/dn2 (x,m) constitutes a QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+1 band edge eigenvalues and eigenfunctions can be obtained analytically. In the limit of m going to 0 or 1, I recover the well known results for the QES double sine-Gordon or double sinh-Gordon equations, respectively. As a by product, I also obtain the bound state eigenvalues and eigenfunctions of the potential V(x) = [ β2/4 - a(a+1) ] sech2 + β (a + ½ ) sechxtanhx in case a is any positive integer or half-integer.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:17692
Deposited On:16 Nov 2010 12:51
Last Modified:17 May 2016 02:17

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