Spiked potentials and quantum toboggans
arXiv:quant-ph/0606166 · doi:10.1088/0305-4470/39/42/008
Abstract
Even if the motion of a quantum (quasi-)particle proceeds along a left-right-symmetric (PT-symmetric) curved path in complex plane, the spectrum of bound states may remain physical, i.e., real and bounded below). We propose a generalization. Firstly, we show how the topologically less trivial (tobogganic) contours may be allowed to live on several sheets of a Riemann surface. Secondly, the specification of a scattering regime is formulated for such a class of models.
revision: 22 pp, 1 fig
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Cited by in corpus (17)
- Conceptual Problems in Scattering from Localized non-Hermitian Potentials
- Scattering theory with localized non-Hermiticities
- Discrete PT-symmetric models of scattering
- Reciprocal and unidirectional scattering of parity-time symmetric structures
- Scattering theory using smeared non-Hermitian potentials
- Hermitian scattering behavior for the non-Hermitian scattering center
- Scattering in the PT-symmetric Coulomb potential
- Quantum toboggans with two branch points
- p-Adic Schrödinger-Type Operator with Point Interactions
- Identification of observables in quantum toboggans
- Origin of branch points in the spectrum of PT-symmetric periodic potentials
- Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
- Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
- Quantum toboggans: models exhibiting a multisheeted PT symmetry
- Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
- Quantum knots
- Planarizable Supersymmetric Quantum Toboggans