Exact solutions of the Schrödinger equation with the position-dependent mass for a hard-core potential

Dong, Shi‐Hai; Lozada‐Cassou, Marcelo

doi:10.1016/j.physleta.2005.02.008

Cited by 88 publications

(48 citation statements)

References 30 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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“…For references, see e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and those cited therein. Due to the fact that the position-dependent mass m(q) does not commute with the momentum operator p = −id/dq, ambiguity arises in defining a quantum kinetic operator which is formally Hermitian and reduces to the classical kinetic term T = p 2 /2m(q).…”

Section: Introductionmentioning

confidence: 99%

-fold supersymmetry in quantum systems with position-dependent mass

Tanaka¹

2005

J. Phys. A: Math. Gen.

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We formulate the framework of N -fold supersymmetry in one-body quantum mechanical systems with position-dependent mass (PDM). We show that some of the significant properties in the constant-mass case such as the equivalence to weak quasi-solvability also hold in the PDM case. We develop a systematic algorithm for constructing an N -fold supersymmetric PDM system. We apply it to obtain type A N -fold supersymmetry in the case of PDM, which is characterized by the so-called type A monomial space. The complete classification and general form of effective potentials for type A N -fold supersymmetry in the PDM case are given.

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“…The one-dimensional nonrelativistic Schrödinger equation for a bound state is (1) where m is the mass of the particle and is the Planck constant divided by 2π. n is the quantum number or a number of node in wave function .…”

Section: -12mentioning

confidence: 99%

Exactly Solvable Potentials Derived from SWKB Quantization

Sun

2014

Bulletin of the Korean Chemical Society

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The shape invariant potentials are proved to be exactly solvable, i.e. the wave functions and energies of a particle moving under the influence of the shape invariant potentials can be algebraically determined without any approximations. It is well known that the SWKB quantization is exact for all shape invariant potentials though the SWKB quantization itself is approximate. This mystery has not been mathematically resolved yet and may not be solved in a concrete fashion even in the future. Therefore, in the present work, to understand (not prove) the mystery an attempt of deriving exactly solvable potentials directly from the SWKB quantization has been made. And it turns out that all the derived potentials are shape invariant. It implicitly explains why the SWKB quantization is exact for all known shape invariant potentials. Though any new potential has not been found in this study, this brute-force derivation of potentials helps one understand the characteristics of shape invariant potentials.

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Exact solutions of the Schrödinger equation with the position-dependent mass for a hard-core potential

Cited by 88 publications

References 30 publications

Torsion effects on a relativistic position-dependent mass system

Torsion effects on a relativistic position-dependent mass system

-fold supersymmetry in quantum systems with position-dependent mass

Exactly Solvable Potentials Derived from SWKB Quantization

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