Spiked potentials and quantum toboggans

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Spiked potentials and quantum toboggans

Even if the motion of a quantum (quasi-)particle proceeds along a left–rightsymmetric (PT -symmetric) curved path C = R in complex plane C, the spectrum of bound states may remain physical (i.e., real and bounded below). A generalization is outlined. First, we show how the topologically less trivial (tobogganic) contours C may be allowed to live on several sheets of a Riemann surface. Second, t...

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Spiked harmonic quantum toboggans

Quantum particle is assumed located in an analytically perturbed harmonic-oscillator potential. Its motion along certain complex, PT −symmetric “toboggan” paths which N−times encircle the branch point in the origin is studied in both the boundstate and scattering regime.

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Quantum toboggans

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 wi...

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Planarizable Supersymmetric Quantum Toboggans

In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate x giving the so called quantum toboggan models (QTM). The consistent theoretical background of this recipe is briefly review...

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Quantum toboggans with two branch points

In an innovated version of PT −symmetric Quantum Mechanics, wave functions ψ (x) describing quantum toboggans (QT) are defined along complex contours of coordinates x(s) which spiral around the branch points x . In the first nontrivial case with x ) = ±1, a classification is found in terms of certain “winding descriptors” ̺. For some ̺0, a mapping x (s) → y(s) is presented which rectifies the con...

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ژورنال

عنوان ژورنال: Journal of Physics A: Mathematical and General

سال: 2006

ISSN: 0305-4470,1361-6447

DOI: 10.1088/0305-4470/39/42/008