The ODE/IM correspondence and PT-symmetric quantum mechanics

Abstract

A connection between integrable quantum field theory and the spectral theory of ordinary differential equations is reviewed, with particular emphasis being given to its relevance to certain problems in PT-symmetric quantum mechanics.

12 pages, 9 figures. Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como, 18-23 June 2001

References in corpus (19)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• PT-Symmetric Quantum Mechanics
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Supersymmetry and the spontaneous breakdown of PT symmetry
• PT -symmetric harmonic oscillators
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• On the reality of the eigenvalues for a class of PT-symmetric oscillators
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• Functional relations in Stokes multipliers - Fun with $x^6+\alpha x^2$ potential-
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• Ordinary Differential Equations and Integrable Models
• Baxter Equation for Quantum Discrete Boussinesq Equation
• Stokes Multipliers, Spectral Determinants and T-Q relations