Entire functions, PT-symmetry and Voros's quantization scheme

DOI10.30970/ms.54.2.203-210zbMath1454.34003arXiv1510.02504OpenAlexW3113714567MaRDI QIDQ1998986

Alexandre Eremenko

Publication date: 10 March 2021

Published in: Matematychni Studiï (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02504

zbMATH Keywords

entire functions\(PT\)-symmetryStokes multipliersexact quantization scheme

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Explicit solutions, first integrals of ordinary differential equations (34A05) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (2)

PT-symmetric eigenvalues for homogeneous potentials ⋮ On solutions of the Bethe Ansatz for the Quantum KdV model

Cites Work

• Anharmonic oscillators in the complex plane, \(\mathcal{PT}\)-symmetry, and real eigenvalues
• Asymptotics of eigenvalues of non-self-adjoint Schrödinger operators on a half-line
• On the relation between Stokes multipliers and the \(T\)-\(Q\) systems of conformal field theory
• On the reality of the eigenvalues for a class of \(\mathcal{PT}\)-symmetric oscillators
• Convergence of an exact quantization scheme
• Research questions on meromorphic functions and complex differential equations
• 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
• Entire functions with two radially distributed values
• 𝓟𝓣-symmetric quantum mechanics
• Exact quantization condition for anharmonic oscillators (in one dimension)
• Eigenvalues of -symmetric oscillators with polynomial potentials
• The ODE/IM correspondence
• NON-TRIVIAL ENTIRE SOLUTIONS OF THE FUNCTIONAL EQUATION f(λ) + f (ωλ)f(ω -1λ) = 1, ω5 = 1
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