Motion of a particle in a Coulomb plus Aharonov-Bohm potential

Kibler, M.; Négadi, Tidjani

doi:10.1016/0375-9601(87)90369-0

Cited by 47 publications

(27 citation statements)

References 17 publications

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“…In recent years, numerous studies [36][37][38][39][40] have been made in analyzing the bound states of an electron in a Coulomb field with simultaneous presence of Aharanov-Bohm (AB) [41] field, and/or a magnetic Dirac monopole [42], and Aharanov-Bohm plus oscillator (ABO) systems. In most of these studies, the eigenvalues and eigenfunctions are obtained by means of seperation of variables in spherical or other orthogonal curvilinear coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Ikhdair¹,

Sever

2008

Int. J. Mod. Phys. C

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We present analytically the exact energy bound-states solutions of the Schrödinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.

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Section: Introductionmentioning

confidence: 99%

Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Ikhdair¹,

Sever

2008

Int. J. Mod. Phys. C

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“…where B is the normalization constant and the weight function ρ( ) must satisfy the condition [41][42][43][44][45] …”

Section: Basic Concepts Of the Methodsmentioning

confidence: 99%

“…In recent years, numerous studies [41][42][43][44][45] have been made in analyzing the bound states of an electron in a Coulomb field with the simultaneous presence of an Aharanov-Bohm (AB) [46] field, and/or a magnetic Dirac monopole [47], and Aharanov-Bohm plus oscillator (ABO) systems. These contributions were achieved by solving the SE through separating the variables in spherical, parabolic or other orthogonal curvilinear coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Ikhdair¹,

Sever

2008

Open Physics

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Abstract:A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ringshaped potential, is solved. It has the formThe energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions. PACS

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“…Finally, the so-called ABC and ABO systems (which are companions of the V Q and U Q systems concerning an Aharonov-Bohm plus a Coulomb potential and an Aharonov-Bohm plus an oscillator potential, respectively) have been the object of several investigations in a nonrelativistic formulation [15][16][17][18] as well as in a relativistic one [19].…”

Section: Introductionmentioning

confidence: 99%

Classical trajectories for two ring‐shaped potentials

Kibler

Lamot

Winternitz

1992

Int J of Quantum Chemistry

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The present paper deals with the classical trajectories for two super-integrable systems : a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to ringshaped potentials. They admit two maximally super-integrable systems as limiting cases, viz, the isotropic harmonic oscillator system and the Coulomb-Kepler system in three dimensions. The planarity of the trajectories is studied in a systematic way. In general, the trajectories are quasi-periodic rather than periodic. A constraint condition allows to pass from quasi-periodic motions to periodic ones. When written in a quantum mechanical context, this constraint condition leads to new accidental degeneracies for the two systems studied.2

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Motion of a particle in a Coulomb plus Aharonov-Bohm potential

Cited by 47 publications

References 17 publications

Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Classical trajectories for two ring‐shaped potentials

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