A complex periodic QES potential and exceptional points
نویسنده
چکیده
We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 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 Mathieu equation. Short title: Complex periodic QES potential
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ar X iv : 0 71 0 . 18 02 v 2 [ qu an t - ph ] 1 2 N ov 2 00 7 A complex periodic QES potential and exceptional points
We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 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...
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We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 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...
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