Quantum toboggans with two branch points

Abstract

Wave functions describing quantum toboggans with two branch points (QT2) are defined along complex contours of coordinates which spiral around these branch points. The classification of QT2 is found in terms of certain ``winding descriptors" $\varrho$. A mapping $x^{(\varrho )}(s)\to y^{(0)}(s)$ is then presented which rectifies the contours for a subset of the simplest $\varrho ={\varrho }_0$.

19pp, 3 figs, presented also as a part of the lecture for QTS-5 conference in Valladolid, Spain, during July 22-28, 2007 (see its webpage http://tristan.fam.cie.uva.es/qts5)

References in corpus (9)

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• PT-Symmetric Quantum Mechanics
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• PT -symmetric harmonic oscillators
• On the reality of the eigenvalues for a class of PT-symmetric oscillators
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• Spiked potentials and quantum toboggans
• Quantum toboggans
• Dynamics of charged fluids and 1/L perturbation expansions

Cited by in corpus (10)

• $J$-self-adjoint operators with $\mathcal{C}$-symmetries: extension theory approach
• On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
• Identification of observables in quantum toboggans
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Quantum toboggans: models exhibiting a multisheeted PT symmetry
• Sturm-Schroedinger equations: formula for metric
• Quantum knots
• Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
• Planarizable Supersymmetric Quantum Toboggans
• PT-symmetric knotting of coordinates: a new, topological mechanism of quantum confinement