A PT-invariant potential with complex QES eigenvalues

2000/06/28 by Avinash Khare, Bhabani Prasad Mandal · 165 citations
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Invariant (physics) #Mathematical physics #Nonlinear Waves and Solitons #Particle physics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/s0375-9601(00)00409-6

published in Physics Letters A 272(1-2), 53-56 (Elsevier BV) · 8 pages, Latex, No fig, To appear in PLA(2000)

arxiv created 2000/06/28 · openalex publication_date 2000/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the quasi-exactly solvable eigenvalues of the Schrödinger equation for the PT-invariant potential V(x) = -(ζ\cosh 2x -iM)² are complex conjugate pairs in case the parameter M is an even integer while they are real in case M is an odd integer. We also show that whereas the PT symmetry is spontaneously broken in the former case, it is unbroken in the latter case.

Citations

• Complex periodic potentials with real band spectra
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• A family of complex potentials with real spectrum

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• Emergence of Hermitian topology from non-Hermitian knots
• PT-symmetric pseudo-perturbation recipe: an imaginary cubic oscillator with spikes
• Various scattering properties of a new PT-symmetric non-Hermitian potential
• PT-Symmetric Solutions of Schrödinger Equation with Position-Dependent Mass via Point Canonical Transformation
• A new solvable complex PT-symmetric potential
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• QES SYSTEMS, INVARIANT SPACES AND POLYNOMIALS RECURSIONS