Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation

Karayer, H.; Demirhan, D.; Büyükkılıç, Fevzi

doi:10.1063/1.5022008

Cited by 39 publications

(22 citation statements)

References 11 publications

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“…[11], where the authors studied the quarkonium dissociation in anisotropic plasma in hot and dense media by analytically solving the multidimensional Schrödinger equation via the NU method for the real part of the potential. The NU method was successfully applied for solving the radial Schrödinger equation in the presence of an external magnetic field and the Aharonov-Bohm flux fields in [12,13]. The inverse square root potential, which is a long-range potential and a combination of the Coulomb, linear, and harmonic potentials, is often used to describe quarkonium states.…”

Section: Introductionmentioning

confidence: 99%

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

Ahmadov

Abasova

Orucova

2021

Advances in High Energy Physics

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In this paper, we study the finite temperature-dependent Schrödinger equation by using the Nikiforov-Uvarov method. We consider the sum of the Cornell, inverse quadratic, and harmonic-type potentials as the potential part of the radial Schrödinger equation. Analytical expressions for the energy eigenvalues and the radial wave function are presented. Application of the results for the heavy quarkonia and B c meson masses are in good agreement with the current experimental data except for zero angular momentum quantum numbers. Numerical results for the temperature dependence indicates a different behaviour for different quantum numbers. Temperature-dependent results are in agreement with some QCD sum rule results from the ground states.

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Section: Introductionmentioning

confidence: 99%

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

Ahmadov

Abasova

Orucova

2021

Advances in High Energy Physics

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“…Remark that this potential corresponds to a combination of Coulomb, oscillator and linear potentials, together with a centrifugal term. This potential is used to describe the quarkonium [30,31] and a two-electron quantum dot [32].…”

Section: From the Biconfluent Heun Equation To A Schrödinger Equationmentioning

confidence: 99%

“…This potential V 2 (x) includes a long range term V (x) = −α/ √ x that has been studied in [30]. Choosing appropriate values of the parameters, the term x 3 2 can be eliminated.…”

Section: From the Biconfluent Heun Equation To A Schrödinger Equationmentioning

confidence: 99%

Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians

et al. 2019

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We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum optics and a family of quasi-exactly solvable Schrödinger equations. The connection between them is stablished through the biconfluent Heun equation. We found that each invariant n-dimensional subspace of Tavis-Cummings Hamiltonian corresponds either to n potentials, each with one known solution, or to one potential with n-known solutions. Among these Schrödinger potentials appear the quarkonium and the sextic oscillator.PACS: 42.65.Ky, 02.20.Sv, 03.65.Fd, 02.30.Gp IntroductionThe main objective of this paper is to show a direct method to connect quantum optics Hamiltonians with quasi-exactly solvable (QES) one-dimensional Schrödinger equations by considering the case of a trilinear Hamiltonian. In principle, these two topics are quite far away since optical Hamiltonians make use of operators corresponding to the radiation modes or to the interacting atoms with a number of allowed transitions, while Schrödinger equations describe a (one dimensional, in this case) particle under an external potential. However, the relation between the solutions of quantum optical Hamiltonians and Schrödinger wavefunctions has been already considered in some references (see [1][2][3]). Our purpose in this work is to illustrate this connection in a clear and explicit way, including all the relevant details.The quantum optical Hamiltonians we consider are modifications of the Jaynes-Cummings model [4] in the rotating wave approximation (or RWA) describing the interaction of a onemode quantum radiation field with a two-level atom. Here, we will specially be concerned with the Dicke or Tavis-Cummings (TC) Hamiltonians which take into account the interaction of radiation with a population of two-level atoms [5] (other cases such as three-level atoms can also be considered, but it will not be done here). With the help of the Schwinger representation we

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“…[11], where the authors studied the quarkonium dissociation in an anisotropic plasma in the hot and dense media by analytically solving the multidimensional Schrödinger equation via NU method for the real part of the potential. NU method was successfully applied for solving the radial Schrödinger equation in the presence of external magnetic field and Aharonov-Bohm flux fields in [12,13]. The inverse square root potential which is a long-range potential and a combination of Coulomb, linear, and harmonic potentials which is often used to describe quarkonium states.…”

Section: Introductionmentioning

confidence: 99%

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

Ahmadov¹,

Abasova²,

Orucova³

2021

Preprint

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In this paper we study the finite temperature dependent Schrödinger equation by using the Nikiforov-Uvarov method. We consider the sum of Cornell, inverse quadratic and harmonic type potential as the potential part of the radial Schrödinger equation. Analytical expressions for the energy eigenvalues and the radial wave function are presented. Application of the results for the heavy quarkonia and B c meson masses are well agreement with the current experimental data whereas zero angular momentum quantum numbers. Numerical results for the temperature dependence indicates different behaviour for different quantum numbers. Temperature dependent results are in agreement with some QCD sum rules results for the ground states.

show abstract

Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation

Cited by 39 publications

References 11 publications

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

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