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

Alhaidari, A. D.

doi:10.1103/physreva.66.042116

Cited by 249 publications

(255 citation statements)

References 62 publications

(30 reference statements)

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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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“…In most applications, this PCT is used in the following way (see, e.g., [36]). One starts from a given exactly solvable constant-mass Schrödinger equation, hence from some known U (u), ε n , and φ n (u).…”

Section: General Methodsmentioning

confidence: 99%

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Quesne¹

2009

SIGMA

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Abstract. On using the known equivalence between the presence of a position-dependent mass (PDM) in the Schrödinger equation and a deformation of the canonical commutation relations, a method based on deformed shape invariance has recently been devised for generating pairs of potential and PDM for which the Schrödinger equation is exactly solvable. This approach has provided the bound-state energy spectrum, as well as the ground-state and the first few excited-state wavefunctions. The general wavefunctions have however remained unknown in explicit form because for their determination one would need the solutions of a rather tricky differential-difference equation. Here we show that solving this equation may be avoided by combining the deformed shape invariance technique with the point canonical transformation method in a novel way. It consists in employing our previous knowledge of the PDM problem energy spectrum to construct a constant-mass Schrödinger equation with similar characteristics and in deducing the PDM wavefunctions from the known constantmass ones. Finally, the equivalence of the wavefunctions coming from both approaches is checked.

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“…It is worth pointing out that in the context of condensed matter physics, scalar potentials proportional to the inverse of the radial distance have been studied with 1-dimensional systems [45][46][47][48][49], molecules [50][51][52], pseudo-harmonic interactions [53,54], position-dependent mass systems [55][56][57], the Kratzer potential [58][59][60]. Other contexts are the propagation of gravitational waves [61], quark models [62], atoms with magnetic quadrupole moment [34] and relativistic quantum mechanics [63][64][65][66][67].…”

Section: Scalar Potential Proportional To the Inverse Of The Ra-dmentioning

confidence: 99%

Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

Fonseca

Bakke

2016

Few-Body Syst

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The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schrödinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schrödinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.

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

Cited by 249 publications

References 62 publications

Torsion effects on a relativistic position-dependent mass system

Torsion effects on a relativistic position-dependent mass system

Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations

Quantum Effects on an Atom with a Magnetic Quadrupole Moment in a Region with a Time-Dependent Magnetic Field

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