A complex periodic QES potential and exceptional points

2007/10/31 by Bijan Bagchi, B. Bagchi, C. Quesne +2 · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/41/2/022001

published as J.Phys.A41:022001,2008 · 9 pages, no figure, published version

openalex publication_date 2007/12/19 · arxiv created 2007/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We show that the complex -symmetric periodic potential V ( x ) = −(iξsin 2 x + 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 the Mathieu equation.

Citations

• Making Sense of Non-Hermitian Hamiltonians
• The Eigenvalues of Mathieu's Equation and their Branch Points

Cited by

• A non-Hermitian PT symmetric Bose–Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Non-Hermitian Hamiltonians of Lie algebraic type