Bound states in the continuum from supersymmetric quantum mechanics

Pappademos, John; Sukhatme, U.; Pagnamenta, A.

doi:10.1103/physreva.48.3525

Cited by 101 publications

(92 citation statements)

References 22 publications

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“…This transformation can be applied to a free-particle extended state to yield a different potential where the corresponding state keeps its positive energy (remaining in the continuum) but becomes spatially localized [189][190][191] . In some cases, this SUSY method is equivalent to von Neumann and Wigner's approach and the Gel'fand-Levitan approach 192 .…”

Section: Potential Engineeringmentioning

confidence: 99%

Bound states in the continuum

et al. 2016

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Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

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Section: Potential Engineeringmentioning

confidence: 99%

Bound states in the continuum

et al. 2016

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“…However, since the original work by von Neumann and Wigner [14], it is known that in certain potentials one can find bound (normalizable) states with an energy embedded inside the continuum of scattered states. Bound states in the continuum (BIC) have been generally regarded as fragile states occurring in a few special systems with tailored potential [15,16,17,18], generally decaying into resonance states by small perturbations [19] and thus of low physical relevance. In the simplest case, BIC can arise from destructive quantum interference of the decay channels to the continuum [20,21,22,23], for example by virtue of a simple symmetry constraint [24].…”

Section: Introductionmentioning

confidence: 99%

Tamm–Hubbard surface states in the continuum

Longhi

Valle

2013

J. Phys.: Condens. Matter

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Abstract. In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential V at the lattice boundary. Such thresholdless surface states, that can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential V is attractive (repulsive) and the particle-particle Hubbard interaction U is repulsive (attractive), i.e. for U V < 0.

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“…In this subsection, we show how one can start from a potential with a continuum of energy eigenstates, and use the methods of SUSY QM to generate families of potentials with bound states in the continuum [BICs] [115]. Basically, one is using the technique of generating isospectral potentials (discussed in Sec.…”

Section: Bound States In the Continuummentioning

confidence: 99%

“…The question of singular superpotentials has also been discussed in some detail within SUSY QM formalism [110,111,112,113,114]. Very recently it has been shown that SUSY QM offers a systematic method [115] for constructing bound states in the continuum [116,117,118].…”

Section: Introductionmentioning

confidence: 99%

Parasupersymmetry in quantum mechanics

Khare

1993

Journal of Mathematical Physics

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In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all 1 have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.

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Bound states in the continuum from supersymmetric quantum mechanics

Cited by 101 publications

References 22 publications

Bound states in the continuum

Bound states in the continuum

Tamm–Hubbard surface states in the continuum

Parasupersymmetry in quantum mechanics

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