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GAZI UNIVERSITY JOURNAL OF SCIENCE

THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL

A. N. Ikot, Eser Olğar, HASSAN HASSANABADI

Published Dec 19, 2016• 1 citation
OpenAlex

Abstract

In this paper, we study the Schrödinger equation with the generalized Hulthen potential plus a new ring shaped potential. We obtained approximately the bound state energy spectra and the corresponding wave function using the functional analysis method. We use the well-known Hellmann-Feynmann theorem to calculate the expectation values for ,, and .We also discussed the special case of the potential which is consistent with the results found in the literature.

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Eigensolution and Expectation Values of the Hulthen and Generalized Inverse Quadratic Yukawa Potential

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.

Jordan Journal of Physics•Jun 30, 2022•7 citations
In this paper, we study the Schrödinger equation with the generalized Hulthen potential plus a new ring shaped potential. We obtained approximately the bound state energy spectra and the corresponding wave function using the functional analysis method. We use the well-known Hellmann-Feynmann theorem to calculate the expectation values for ,, and .We also discussed the special case of the potential which is consistent with the results found in the literature.
In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.
In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
Abstract In this study, we investigated the approximate analytical bound state solutions of the Schrödinger equation, considering a linear combination of the deformed (Hulthén 1942 Ark. Mat. Astron. Fys. 28A 671) potential and the generalized (Kratzer 1920 Z. Phys. 3 289–307) potential. The analysis was performed within the path-integral formalism. Using an appropriate approximation to evaluate the centrifugal term, we derived the energy spectrum and normalized wave functions of the bound states from the poles of the Green’s function and its residues. To evaluate the accuracy and applicability of the derived expressions, we discuss several limiting cases of the potential and carry out numerical calculations of the energy levels, complemented by illustrative plots for selected diatomic molecules.
Abstract The approximate bound state solutions of Schrödinger equation with linear combination of a q-deformed Hulthén potential plus screened Kratzer potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briefly and it is found that obtained results are in good agreement with those obtained in the literature.
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.