Wave function for smooth potential and mass step

Dekar, Liès; Chétouani, L.; Hammann, T. F.

doi:10.1103/physreva.59.107

Cited by 131 publications

(96 citation statements)

References 20 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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“…Mass 63 has been subject to earlier investigations, for details see [7,9,30]. In this example we want give the transformation for mapping the TDSE with effective mass (63) onto a TDSE with constant mass:…”

Section: Example 2: Step-like Massmentioning

confidence: 99%

“…• Step 1: Determination of the new coordinate u = u(x, t) via (30). This is necessary, because for the subsequent calculation of the transformation function f we need to know the relation between u and x for expressingM in terms of x.…”

Section: Example 1: Power Law Massesmentioning

confidence: 99%

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Schulze-Halberg

2005

Open Physics

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Abstract:We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

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“…Examples of these studies are the binding of heavy quarks [5,6], the vibrational spectrum of diatomic molecules [7] and oscillations of atoms in crystal lattices by mapping them as a position-dependent mass system [8][9][10][11]. In recent decades, the relativistic generalization of the harmonic oscillator has attracted a great deal of attention whose model proposed by Moshinsky and Szczepaniak [12] is the best known for Dirac particles.…”

Section: Introductionmentioning

confidence: 99%

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

2016

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The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the KleinGordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.

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Wave function for smooth potential and mass step

Cited by 131 publications

References 20 publications

Torsion effects on a relativistic position-dependent mass system

Torsion effects on a relativistic position-dependent mass system

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

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