Quantum toboggans: models exhibiting a multisheetedPT—symmetry

2007/10/08 by Miloslav Znojil
Mathematics · Physics and Astronomy · #Boundary (topology) #Generalization #Geometry #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Symmetry (geometry) #Wave function #quant-ph

paper · pdf · doi:10.1088/1742-6596/128/1/012046

published as J. Phys.: Conference Series 128 (2008) 012046 (12pp) · 16 pp, 5 figs. Written version of the talk given during 5th International Symposium on Quantum Theory and Symmetries, University of Valladolid, Spain, July 22 - 28 2007, webpage http://tristan.fam.uva.es/~qts5

arxiv created 2007/10/08 · openalex publication_date 2008/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A generalization of the concept of PT —symmetric Hamiltonians H = p 2 + V ( x ) is presented. For the usual analytic potentials V ( x ) (with singularities) and for the recently widely accepted ' PT —symmetric' asymptotic boundary conditions for wave functions ψ( x ) (selected inside a pair of complex wedges generalizing the usual x → ± ∞ asymptotics), non-equivalent quantum toboggans are defined as integrated along topologically different paths C of coordinates x ε Cl .

Citations

• On The Reality Of The Eigenvalues For A Class Of PT-Symmetric Oscillators
• Quantum toboggans with two branch points
• -symmetric quantum toboggans
• Making sense of non-Hermitian Hamiltonians
• Propagation of electromagnetic waves in linear media and pseudo-hermiticity
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Generation of Exactly Solvable Non-Hermitian Potentials with Real Energies
• Complex Lagrangians and phantom cosmology
• Physics of Nonhermitian Degeneracies