A complex periodic QES potential and exceptional points

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dc.creatorBagchi, B.
dc.creatorQuesne, C.
dc.creatorRoychoudhury, R.
dc.date2007-10-09
dc.date2007-12-20
dc.date.accessioned2026-07-07T11:12:07Z
dc.date.available2026-07-07T11:12:07Z
dc.descriptionWe show that the complex $\cal PT$-symmetric periodic potential $V(x) = - ({\rm i} ξ\sin 2x + N)^2$, where $ξ$ is real and $N$ is a positive integer, is quasi-exactly solvable. For odd values of $N \ge 3$, it may lead to exceptional points depending upon the strength of the coupling parameter $ξ$. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of the exceptional points derived in our scheme is consistent with known branch-point singularities of the Mathieu equation.
dc.description9 pages, no figure, published version
dc.identifierhttps://arxiv.org/abs/0710.1802
dc.identifierhttp://arxiv.org/abs/0710.1802
dc.identifierJ.Phys.A41:022001,2008
dc.identifierdoi:10.1088/1751-8113/41/2/022001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/191274
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleA complex periodic QES potential and exceptional points
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