Exact solvability of potentials with spatially dependent effective masses

Dutra, A. de Souza; Almeida, C. A. S.

doi:10.1016/s0375-9601(00)00533-8

Cited by 244 publications

(212 citation statements)

References 39 publications

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“…At present days, several discussions can be found in the literature with the purpose of showing different ways of dealing with position dependent-mass systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Another context has been discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Torsion effects on a relativistic position-dependent mass system

Vitória

Bakke

2016

Gen Relativ Gravit

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We analyse a relativistic scalar particle with a position-dependent mass in a spacetime with a space-like dislocation by showing that relativistic bound states solutions can be achieved. Further, we consider the presence of the Coulomb potential and analyse the relativistic position-dependent mass system subject to the Coulomb potential in the spacetime with a space-like dislocation. We also show that a new set of relativistic bound states solutions can be obtained, where there also exists the influence of torsion of the relativistic energy levels. Finally, we investigate an analogue of the Aharonov-Bohm effect for bound states in this position-dependent mass in a spacetime with a space-like dislocation.

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Section: Introductionmentioning

confidence: 99%

Torsion effects on a relativistic position-dependent mass system

Vitória

Bakke

2016

Gen Relativ Gravit

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“…Recently, several contributions have emerged in the literature where some of the above-mentioned developments in nonrelativistic quantum mechanics were extended to the case of spatially dependent mass distribution [10][11][12][13][14]. The motivation for obtaining exact solutions of the wave equation with position dependent mass comes from the wide range of applications of these solutions in various areas of material science and condensed matter.…”

Section: Introductionmentioning

confidence: 99%

“…Coordinate transformation in supersymmetric quantum mechanics were used in [12] to generate isospectral potentials with position dependent mass. The ordering ambiguity of the mass and momentum operator and its effect on the exact solutions was addressed in [13] where several examples are considered. so(2,1) Lie algebra as a spectrum generating algebra and as a potential algebra was used in [14] to obtain exact solutions of the effective mass wave equation.…”

Section: Introductionmentioning

confidence: 99%

Solutions of the nonrelativistic wave equation with position-dependent effective mass

2002

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Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrödinger equations with constant mass using point canonical transformation. The Oscillator, Coulomb, and Morse class of potentials are considered.

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“…In recent times a good number of articles have been published [10,11,12,13,14,15,16,17,18,19] in this field. The Schrödinger equation with position-dependent mass has been studied in the contexts of supersymmetry, shapeinvariance, Lie algebra, point-canonical transformation, etc.…”

Section: Introductionmentioning

confidence: 99%