Beyond the WKB approximation in PT-symmetric quantum mechanics

Abstract

The mergings of energy levels associated with the breaking of PT symmetry in the model of Bender and Boettcher, and in its generalisation to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously-observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrodinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero.

29 pages, Latex, many figures. v2: sign typos fixed, and a reference added

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• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Conditional observability
• Geometric aspects of the ODE/IM correspondence
• Exceptional points in quantum and classical dynamics
• Kurt Symanzik - a stable fixed point beyond triviality
• Spiked potentials and quantum toboggans
• Analysis of the interaction of an electron with radial electric fields in the presence of a disclination
• PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Structure, Time Propagation and Dissipative Terms for Resonances
• Deforming the ODE/IM correspondence with $\mathrm{T}\bar{\mathrm{T}}$
• A semiclassical treatment of the interaction of non-uniform electric fields with the electric quadrupole moment of a neutral particle
• Anomalous real spectra of non-Hermitian quantum graphs in strong-coupling regime
• Aspects of the ODE/IM correspondence
• Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory
• On the ODE/IM correspondence for minimal models
• Classification of the conditionally observable spectra exhibiting central symmetry
• PT-symmetric eigenvalues for homogeneous potentials
• Perturbation-based Non-perturbative Method
• A(2|1) spectral equivalences and nonlocal integrals of motion
• Planarizable Supersymmetric Quantum Toboggans