Spiked potentials and quantum toboggans

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

References in corpus (1)

• Scattering by PT-symmetric non-local potentials

Cited by in corpus (8)

• Scattering theory with localized non-Hermiticities
• Discrete PT-symmetric models of scattering
• Scattering theory using smeared non-Hermitian potentials
• Scattering in the PT-symmetric Coulomb potential
• Quantum toboggans with two branch points
• Identification of observables in quantum toboggans
• Quantum toboggans: models exhibiting a multisheeted PT symmetry
• Quantum knots