PT-symmetric eigenvalues for homogeneous potentials

DOI10.1063/1.5016390zbMath1390.81145arXiv1711.06910OpenAlexW3098809251MaRDI QIDQ4565454

Andrei Gabrielov, Alexandre Eremenko

Publication date: 12 June 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.06910

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20)

Related Items (2)

Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Non-real eigenvalues of the harmonic oscillator perturbed by an odd, two-point interaction

Cites Work

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• Asymptotics of eigenvalues of non-self-adjoint Schrödinger operators on a half-line
• Entire functions, PT-symmetry and Voros's quantization scheme
• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• The potential (iz)m generates real eigenvalues only, under symmetric rapid decay boundary conditions
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Beyond the WKB approximation in -symmetric quantum mechanics
• 𝓟𝓣-symmetric quantum mechanics
• The ODE/IM correspondence

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