Bound states in the continuum from supersymmetric quantum mechanics

In this paper, we investigate phase rigidity of one-dimensional point interactions. With the aid of supersymmetric quantum mechanics (SUSYQM) we generate family of isospectral potentials describing point interactions. We than demonstrate that for SUSYQM generated bound states in the continuum (BIC) phase rigidity is always zero, while for bound states from discrete part of spectrum phase rigidity may vary from zero to unity, depending on the strength of point interaction.

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BOUND STATES IN CONTINUUM GENERATED BY POINT INTERACTION AND SUPERSYMMETRIC QUANTUM MECHANICS

Modern Physics Letters B ◽

10.1142/s0217984912501771 ◽

2012 ◽

Vol 26 (27) ◽

pp. 1250177 ◽

Cited By ~ 7

Author(s):

S. Lj. S. KOČINAC ◽

V. MILANOVIĆ

Keyword(s):

Quantum Mechanics ◽

Kinetic Energy ◽

Bound States ◽

Energy Operator ◽

Bound State ◽

Point Interaction ◽

Supersymmetric Quantum Mechanics ◽

Kinetic Energy Operator ◽

Point Interactions ◽

The Continuum

Four-parameter family of point interactions represent all possible self-adjoint extensions of kinetic energy operator. We demonstrate a method for generating a bound state in the continuum of point interactions which relies on supersymmetric quantum mechanics (SUSYQM). Both zero and nonzero transparency cases are considered.

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Bound states at threshold in supersymmetric quantum mechanics

Nuclear Physics B ◽

10.1016/s0550-3213(97)00804-3 ◽

1998 ◽

Vol 515 (1-2) ◽

pp. 184-202 ◽

Cited By ~ 37

Author(s):

Massimo Porrati ◽

Alexander Rozenberg

Keyword(s):

Quantum Mechanics ◽

Bound States ◽

Supersymmetric Quantum Mechanics

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Bound states in continuum of complex potentials generated by supersymmetric quantum mechanics

Physics Letters A ◽

10.1016/s0375-9601(02)00892-7 ◽

2002 ◽

Vol 300 (6) ◽

pp. 595-602 ◽

Cited By ~ 17

Author(s):

Jovana S. Petrović ◽

Vitomir Milanović ◽

Zoran Ikonić

Keyword(s):

Quantum Mechanics ◽

Bound States ◽

Complex Potentials ◽

Supersymmetric Quantum Mechanics

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SUPERSYMMETRIC QUANTUM MECHANICS APPLIED TO NONRELATIVISTIC QUARK MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x93000606 ◽

1993 ◽

Vol 08 (08) ◽

pp. 1437-1455 ◽

Cited By ~ 5

Author(s):

E.J.O. GAVIN ◽

H. FIEDELDEY ◽

H. LEEB ◽

S.A. SOFIANOS

Keyword(s):

Quantum Mechanics ◽

Bound States ◽

Approximation Scheme ◽

Energy Levels ◽

Supersymmetric Quantum Mechanics ◽

S Wave ◽

Nucleon Spectrum ◽

Quark Potential ◽

Quark Models ◽

Original Potential

We examine the effect of changing the energy levels and normalization constants of bound states corresponding to baryons and mesons in nonrelativistic quark models. We do this by applying the transformations of supersymmetric quantum mechanics (SUSYQM) to the potentials used in these models. In particular, we fit the spectra and leptonic decay widths of [Formula: see text] and [Formula: see text] mesons by modifying several existing [Formula: see text] potentials by means of supersymmetric transformations. It is found that the potentials are unchanged beyond 2 fm, and that fitting the widths induces greater oscillations in the potentials than those generated by adjusting the energy levels only. Transformations of SUSYQM are applied to the hypercentral potential in order to accommodate the Roper resonance in the s-wave nucleon spectrum. The quark-quark potential found by inverting the transformed hypercentral potential via a new exact Abel transform differs significantly from the original potential up to 5 fm from the origin and violates the concavity requirement. The [Formula: see text] potential related to this potential by Lipkin’s rule does not reproduce the meson spectrum. As the Hall-Post lower bound is also accurate for baryons, the results of the application of supersymmetric transformations in this approximation scheme are also considered and compared to the upper bound of the hypercentral approximation.

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ANOMALOUS SUSY QUANTUM MECHANICS, HETEROTIC MODELS AND SCATTERING STATES

Modern Physics Letters A ◽

10.1142/s0217732392002093 ◽

1992 ◽

Vol 07 (25) ◽

pp. 2325-2331

Author(s):

L. J. BOYA ◽

J. CASAHORRÁN ◽

J. G. ESTEVE

Keyword(s):

Quantum Mechanics ◽

Symmetry Breaking ◽

Continuous Spectrum ◽

Real Axis ◽

Bound States ◽

Anomalous Behavior ◽

Heterotic String ◽

Supersymmetric Quantum Mechanics ◽

The Other ◽

Scattering States

We analyze the symmetry breaking associated to anomalous realization of supersymmetry in the context of Supersymmetric Quantum Mechanics (SUSY QM). We show how the supercharge itself might become an anomalous operator in the process of quantization. We study a solvable potential in the Pöschl-Teller class containing both bound states and continuous spectrum. We find a situation reminiscent of the heterotic string: one of the two SUSY partners lives in the whole real axis while the other restricts itself to the half-line. Peculiarities of the model include negative energies, incomplete pairing of states and anomalous behavior for the phase shifts in scattering.

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SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

International Journal of Modern Physics A ◽

10.1142/s0217751x95001261 ◽

1995 ◽

Vol 10 (18) ◽

pp. 2683-2702 ◽

Cited By ~ 133

Author(s):

A.A. ANDRIANOV ◽

M.V. IOFFE ◽

F. CANNATA ◽

J.-P. DEDONDER

Keyword(s):

Quantum Mechanics ◽

Bound States ◽

Scattering Amplitude ◽

Scattering Problem ◽

Higher Order ◽

Supersymmetric Quantum Mechanics ◽

Self Similarity ◽

Systematic Analysis ◽

Higher Derivative ◽

Reflectionless Potential

In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most general supercharges involving higher order derivatives are introduced, leading to an algebra which incorporates a higher order polynomial of the Hamiltonian. We investigate the condition for irreducibility of such a higher order generator to a product of standard first derivative Darboux transformations. As a new example of application of this approach we study the quantum-mechanical radial problem including the scattering amplitudes. We also investigate the links between this higher derivative SUSY and a q-deformed supersymmetric quantum mechanics and introduce the notion of self-similarity in momentum space. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.

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