The energy eigenvalues of the Kratzer potential in the presence of a magnetic field

Aygun, M.; Bayrak, O.; Boztosun, I.; Şahin, Yılmaz

doi:10.1140/epjd/e2011-20319-5

Cited by 44 publications

(21 citation statements)

References 31 publications

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“…We follow Refs. [32,33], the parameters A n , B n and C n must satisfy the determinant relation for a nontrivial solution:…”

Section: Exact Solution To a General Potential Form Under External Fimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Recently, the 2D solution of the Schrödinger equation for the Kratzer potential with and without the presence of a constant magnetic field has been studied for the first time within the framework of the asymptotic iteration method (AIM) [33]. Effect of constant magnetic field on the energy eigenvalues of a particle moving under the Kratzer potential was precisely presented by Aygun et al [33]. Furthermore, we have studied the spectral properties of the quantum dots by solving the Schrödinger equation for the anharmonic oscillator potential and superposition of pseudoharmonic-linear-Coulomb potential in presence/absence of external uniform magnetic and AB flux fields in the framework of the Nikiforov-Uvarov (NU) method and analytical exact iteration method (AEIM) [34].…”

Section: Introductionmentioning

confidence: 99%

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Nonrelativistic molecular models under external magnetic and AB flux fields

2015

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By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary m-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov-Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We calculate the energy levels of some diatomic molecules in the presence and absence of external magnetic and AB flux fields using different potential models. We found that the effect of the Aharonov-Bohm field is much as it creates a wider shift for m = 0 and its influence on m = 0 states is found to be greater than that of the magnetic field. To show the accuracy of the present model, a comparison is made with those ones obtained in the absence of external fields. An extension to 3-dimensional quantum system have also been presented.1 describing the molecular vibrations is important in studying the dynamical variables of diatomic molecules [3]. This potential have a wide applications in various fields of physics and chemistry such as molecular physics, solid-state physics, chemical physics, quantum chemistry, the molecular dynamics study of linear diatomic molecules and the theoretical works on the spectral properties of a diatomic molecule system [4]. Therefore, we found that it is necessary to study the exact bound state solutions of the two-dimensional (2D) solution of the Schrödinger equation for these potentials under the influence of external magnetic and Aharonov-Bohm fields. The 2D hydrogen model was treated as an atomic spectroscopy and used as a simplified model of the ionization process of the highly excited 3D hydrogen atom by circular-polarized microwaves [5]. The field-free relativistic Coulomb interaction has been studied by many authors by using various techniques [6, 7, 8]. The nonrelativistic H-like atom under the influence of magnetic field has been the subject of study over the past years [9, 10, 11]. In the presence of a low magnetic field, the quasi-classical solution of the Dirac equation has been obtained by factorization method [12]. In the framework of the variational method, the ground-state Dirac energies and relativistic spinless lowest few states have been calculated for arbitrary strength values of magnetic field [13, 14, 15]. The Klein-Gordon wave equation was solved exactly for particular values of magnetic field in which the wave function can be expressed in closed analytical form [16]. The polynomial solutions of the Schrödinger equation was obtained for the ground-state and a few first excited states of 2D hydrogenic atoms for particular values of the magnetic field strength perpendicular to the plane of transversal motion of the electron using a relativistic wave function [17]. Recently, within the framework of power-series solutions, the Klein-Gordon and Dirac equations have beensolved for the 2D hydrogen-like systems when an arbitrary external magnetic field is applied [18]. For particular values of magnetic field B, it is found that the exact ...

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“…We follow Refs. [32,33], the parameters A n , B n and C n must satisfy the determinant relation for a nontrivial solution:…”

Section: Exact Solution To a General Potential Form Under External Fimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonrelativistic molecular models under external magnetic and AB flux fields

2015

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“…If one obtain the wave function for investigated system, it can be obtained crucial information regarding the system. Thus, a large number of studies have been performed in order to solve the eigenvalue equation and to determine the correction on the energy eigenvalues (EEs) in a MF (Villalba & Pino 2001;Aygun et al 2012;Villalba & Pino 1998;Aygun et al 2010;Taut 1995). These studies were made possible due to the technological advances in nanofabrication technology, which has enabled the creation of lowdimensional structures such as quantum wires, quantum dots, and quantum wells in semiconductor physics (Demel et al 1990;Zhu et al 1997;Blanter et al 1996;Johnson 1995;Killingbeck & Jolicard 2009).…”

Section: Introductionmentioning

confidence: 99%

The energy eigenvalues of the exponential cosine screened Coulomb potential with magnetic field

Aygun¹

2015

Bitlis Eren University Journal of Science and Technology

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In the present study, we examine two dimensional solution of the Schrödinger equation for the exponential cosine screened Coulomb potential in a magnetic field. We apply the asymptotic iteration method to obtain energy eigenvalues. Since this equation has no analytical solution, the energy eigenvalues have been numerically obtained for different screening parameter, the Larmor frequency and the strength coupling constant. Effect of the magnetic field on the energy eigenvalues is precisely presented.

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“…Overmore, it is natural to study the relativistic effects of the external magnetic and AB flux fields on the KG equation for pseudo-harmonic oscillator potential, especially for a strong coupling by means of the NU method [32]. The 2D solution of Schrödinger equation for the Kratzer potential with and without the presence of a constant magnetic field is studied within the framework of the asymptotic iteration method [33]. The energy eigenvalues are obtained analytically (numerically) for the absence (presence) of uniform magnetic field case.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields

Ikhdair

Sever

2013

Advances in High Energy Physics

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The Klein-Gordon (KG) equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB) flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL= 0) and AB flux field (ξ=0) cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.

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The energy eigenvalues of the Kratzer potential in the presence of a magnetic field

Cited by 44 publications

References 31 publications

Nonrelativistic molecular models under external magnetic and AB flux fields

Nonrelativistic molecular models under external magnetic and AB flux fields

The energy eigenvalues of the exponential cosine screened Coulomb potential with magnetic field

Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields

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