Hypergeometric functions

Nikiforov, A. F.; Uvarov, V.B.

doi:10.1007/978-1-4757-1595-8_4

Cited by 84 publications

(151 citation statements)

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“…The generalized Nikiforov-Uvarov method represents an expansion of the standard Nikiforov-Uvarov method, with both techniques primarily employed within the realm of quantum mechanics. This approach lies in the determination of eigenvalues and eigenfunctions for a range of equations, including Schrödinger-like and Dirac equations, as well as equations susceptive to transformation into hypergeometric form [52,57,[61][62][63].…”

Section: The Generalized Fractional Nikiforov-uvarov Methodsmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

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In this paper, we study within the structure of Symplectic Quantum Mechanics a bidimensional nonrelativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which consists of Coulomb-type plus linear potentials. First, we solve the Schrödinger equation in the phase space with the linear potential. The solution (ground state) is obtained and analyzed by means of the Wigner function related to Airy function for the c c ¯ meson. In the second case, to treat the Schrödinger-like equation in the phase space, a procedure based on the Bohlin transformation is presented and applied to the Cornell potential. In this case, the system is separated into two parts, one analogous to the oscillator and the other we treat using perturbation method. Then, we quantized the Hamiltonian with the aid of stars operators in the phase space representation so that we can determine through the algebraic method the eigenfunctions of the undisturbed Hamiltonian (oscillator solution), and the other part of the Hamiltonian was the perturbation method. The eigenfunctions found (undisturbed plus disturbed) are associated with the Wigner function via Weyl product using the representation theory of Galilei group in the phase space. The Wigner function is analyzed, and the nonclassicality of ground state and first excited state is studied by the nonclassicality indicator or negativity parameter of the Wigner function for this system. In some aspects, we observe that the Wigner function offers an easier way to visualize the nonclassic nature of meson system than the wavefunction does phase space.

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Section: The Generalized Fractional Nikiforov-uvarov Methodsmentioning

confidence: 99%

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Luz

Petronilo

et al. 2022

Advances in High Energy Physics

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“…Equation (2.10) is the one-dimensional Schrödinger wave equation which can be solved using different methods or techniques. Several researchers have employed or applied various methods or techniques, such as the asymptotic iteration method (AIM) [52,53], the Nikiforov-Uvarov (NU) method [77], supersymmetric quantum mechanics (SUSYQM) [55–57], path integral method (PIM) [78], factorization method [58], exact quantization rule [41] and many more in order to find the exact and approximate solutions of the Schrödinger equation. In this analysis, we approach another method where the eigenvalue solution of equation (2.10) can be expressed as the biconfluent Heun (BCH) functions.…”

Section: Non-relativistic Particles In Point-like Defect With Harmoni...mentioning

confidence: 99%

Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials

Ahmed

2023

Proc. R. Soc. A.

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In this analysis, we study the quantum motions of a non-relativistic particle confined by the Aharonov–Bohm (AB) flux field with harmonic oscillator plus Mie-type potential in a point-like defect. We determine the eigenvalue solution of the particles analytically and discuss the effects of the topological defect and flux field with this potential. This eigenvalue solution is then used in some diatomic molecular potential models (harmonic oscillator plus Kratzer, modified Kratzer and attractive Coulomb potentials) and presented as the eigenvalue solutions. Afterwards, we consider a general potential form (superposition of pseudoharmonic plus Cornell-type potential) in the quantum system and analyse the effects of various factors on the eigenvalue solution. It is shown that the eigenvalue solutions are modified by the topological defect of a point-like global monopole and flux field compared to the results obtained in the flat space.

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“…The above differential equation can solve using a well-known method called the the Nikiforov-Uvarov method [42]. This method is very much helpful in order to find the eigenvalues and eigenfunction of the Schrödinger-like equation, as well as other second-order differential equations of physical interest.…”

Section: Interactions With Inverse Quadratic Yukawa Plus Inverse Squa...mentioning

confidence: 99%

Topological defects with generalized Hulthen–Coulomb-inverse quadratic Yukawa potential on eigenvalue solution under Aharonov–Bohm flux field

Ahmed

2022

Int. J. Geom. Methods Mod. Phys.

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In this work, we solve the radial Schrödinger wave equation in three dimensions under Aharonov–Bohm (AB)-flux field with potential superposition of generalized q-deformed Hulthen potential, Coulomb potential, and inverse quadratic Yukawa potential in a point-like defect. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov (NU) method and analyze the effects of topological defect and the magnetic flux field with this superposed potential. We show an analogous of the AB effect because the eigenvalue solution depends on the geometric quantum phase and bound state solutions are possible under condition. Finally, we utilize the approximate eigenvalue solution to some molecular potential models, such as Deng–Fan potential and inverse quadratic Hulthen potential and analyze the effects on the energy levels and the radial wave functions.

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Hypergeometric functions

Cited by 84 publications

References 0 publications

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Quark-Antiquark Effective Potential in Symplectic Quantum Mechanics

Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials

Topological defects with generalized Hulthen–Coulomb-inverse quadratic Yukawa potential on eigenvalue solution under Aharonov–Bohm flux field

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