Generation of exactly solvable potentials of the D-dimensional position-dependent mass Schrödinger equation using the transformation method

Rajbongshi, H.; Singh, N. Nimai

doi:10.1007/s11232-015-0290-2

Cited by 9 publications

(4 citation statements)

References 32 publications

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“…The systems with position-dependent mass were studied also in the case of spatial dimension D > 1 [24,25,26,27,28,29], particularly, in the context of superintegrable systems [31]. It would be interesting to generalize our approach in this direction, having in mind, particularly, a generalization of Mathiew-Lakshamann model for D > 1 which was studied in [63].…”

Section: Concluding Remarks and Outlookmentioning

confidence: 99%

“…They turn out to be interesting from the point of view of supersymmetric quantum mechanics [13,14,15,16,17], coherent states [18,19,20], and PT-symmetry [21,22,23]. Besides the onedimensional quantum systems with PDM, their multi-dimensional generalizations are considered in the literature [24,25,26,27,28,29], particularly, in the context of superintegrable systems [30,31]. See also refs.…”

Section: Introductionmentioning

confidence: 99%

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Position-dependent mass, finite-gap systems, and supersymmetry

Bravo

Plyushchay

2016

Phys. Rev. D

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The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first order supercharges from the kinetic term alone, while inclusion of the potential term allows also to generate nonlinear supersymmetry with higher order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lamé and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS 2 -related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

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Section: Concluding Remarks and Outlookmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Position-dependent mass, finite-gap systems, and supersymmetry

Bravo

Plyushchay

2016

Phys. Rev. D

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“…For the completeness, we shall mention few papers [87], [88], [89] where the multidimensional Schrödinger equation with PDM was studied beyond the SUSY QM approach. In these papers, the main tool was the point canonical transformation of coordinates which allowed to link the problem with a suitable standard Schrödinger equation with constant mass and rotationally invariant potential.…”

Section: Susy Intertwining Relations For Pdm Hamiltoniansmentioning

confidence: 99%

SUSY method for the three-dimensional Schrödinger equation with effective mass

2016

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“…Solutions of the Schrödinger equation with position dependent mass for the Morse potential are investigated by applying different methods in [46][47][48][49][50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Solutions of Morse potential with position-dependent mass by Laplace transform

Miraboutalebi

2016

J Theor Appl Phys

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In the framework of the position-dependent mass quantum mechanics, the three dimensional Schrödinger equation is studied by applying the Laplace transforms combining with the point canonical transforms. For the potential analogues to Morse potential and via the Pekeris approximation, we introduce the general solutions appropriate for any kind of position dependent mass profile which obeys a key condition. For a specific position-dependent mass profile, the bound state solutions are obtained through an analytical form. The constant mass solutions are also relived.

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Generation of exactly solvable potentials of the D-dimensional position-dependent mass Schrödinger equation using the transformation method

Cited by 9 publications

References 32 publications

Position-dependent mass, finite-gap systems, and supersymmetry

Position-dependent mass, finite-gap systems, and supersymmetry

SUSY method for the three-dimensional Schrödinger equation with effective mass

Solutions of Morse potential with position-dependent mass by Laplace transform

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