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Revista Mexicana de Física

Radial solution of Schrödinger equation with Hulthen-Yukawa-Inverse quadratic potential in a Point-Like defect under AB-flux field

Faizuddin Ahmed

Published May 1, 2023• 0 citations
Publisher

Abstract

In this paper, we determine the approximate eigenvalue solution of the non-relativistic wave equation in the presence of the Aharonov-Bohm flux field with Hulthen-Yukawa-Inverse Quadratic potential in a topological defect via point-like global monopole (PGM) geometry. We use the Greene-Aldrich improved approximation scheme into the centrifugal and reciprocal terms appear in the radial Schrödinger equation. We then solve this radial equation using the parametric Nikiforov-Uvarov method and analyze the effects on the eigenvalue solution. We see that the energy levels and the radial wave functions get modified by the topological defect of a point-like global monopole and the magnetic flux field that shows an analogue of the Aharonov-Bohm effect for the bound state. Finally, we utilize the eigenvalue solution to some potential models, such as Hulthen potential, Hulthen plus Yukawa potential, and Hulthen plus inverse quadratic potential and discuss the results.

DOI
10.31349/revmexfis.69.030401

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In this paper, we determine the approximate eigenvalue solution of the non-relativistic wave equation in the presence of the Aharonov-Bohm flux field with Hulthen-Yukawa-Inverse Quadratic potential in a topological defect via point-like global monopole (PGM) geometry. We use the Greene-Aldrich improved approximation scheme into the centrifugal and reciprocal terms appear in the radial Schrödinger equation. We then solve this radial equation using the parametric Nikiforov-Uvarov method and analyze the effects on the eigenvalue solution. We see that the energy levels and the radial wave functions get modified by the topological defect of a point-like global monopole and the magnetic flux field that shows an analogue of the Aharonov-Bohm effect for the bound state. Finally, we utilize the eigenvalue solution to some potential models, such as Hulthen potential, Hulthen plus Yukawa potential, and Hulthen plus inverse quadratic potential and discuss the results.
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.
We study the nonrelativistic Schrödinger equation for q-deformed Hulthen plus modified inversely quadratic Yukawa potential using the generalized parametric form of NIkiforov-Uvarov method. The energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric function are obtained. We have also discussed four (4) special cases of this potential, i.e. Woods-Saxon, Hulthen, Morse and inversely quadratic potentials. Keywords: Nonrelativistic Schrödinger equation, q-deformed Hulthen potential, modified inversely quadratic Yukawa potential, parametric Nikiforov-Uvarov method.
Abstract: In this study, the Schrödinger equation was solved with a superposition of the Hulthen potential and generalized inverse quadratic Yukawa potential model using the Nikiforov-Uvarov (NU) method. For completeness, we also calculated the wave function. To validate our results, the numerical bound state energy eigenvalues was computed for various principal n and angular momentum l quantum numbers. With the aid of the Hellmann-Feynman theorem, the expressions for the expectation values of the square of inverse of position, r^(-2), inverse of position, r^(-1), kinetic energy, T ̂ and square of momentum, p ̂ are calculated. By adjusting the potential parameters, special cases of the potential were considered, resulting in Generalized Inverse Quadratic Yukawa potential, Hulthen potential, Coulomb potential, Kratzer potential, Inversely Quadratic Yukawa potential and Coulomb plus inverse square potential, respectively. Their energy eigenvalue expressions and numerical computations agreed with the literature. Keywords: Schrödinger equation, Hulthen potential (HP), Generalized inverse quadratic Yukawa potential (GIQYP), Nikiforov-Uvarov method. PACS: 03.65.−w, 03.65.Ca, 03.65.Ge.
The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov—Bohm (AB) field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov—Bohm Coulomb problem.
In this work, the non-relativistic wave equation via the Schrödinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, and the Mie-type potential which have wide applications in different branches of physics and chemistry. We solve the Schrodinger wave equation using the Nikiforov-Uvarov (NU) method and obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them. We show that each non-relativistic energy level gets modified in comparison to the known results obtained in the literature.
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