Quantum toboggans

Abstract

Among all the PT-symmetric potentials defined on complex coordinate contours C(s), the name "quantum toboggan" is reserved for those whose C(s) winds around a singularity and lives on at least two different Riemann sheets. An enriched menu of prospective phenomenological models is then obtainable via the mere changes of variables. We pay thorough attention to the harmonic oscillator example with a fractional screening and emphasize the role of the existence and invariance of its quasi-exact states for different tobogganic C(s).

17 pp., 7 figures

References in corpus (2)

• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator

Cited by in corpus (12)

• Spiked potentials and quantum toboggans
• Behavior of eigenvalues in a region of broken-PT symmetry
• Quantum toboggans with two branch points
• Identification of observables in quantum toboggans
• Negative-energy PT-symmetric Hamiltonians
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Quantum toboggans: models exhibiting a multisheeted PT symmetry
• Quantum knots
• Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
• Spectra of PT-symmetric Hamiltonians on Tobogganic Contours
• Ad hoc physical Hilbert spaces in Quantum Mechanics
• Planarizable Supersymmetric Quantum Toboggans