Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

Abstract

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.

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

“…For example, the Cornell potential which is the combination of the Coulomb potential with linear terms is used in studying the mass spectra for coupled states and for the electromagnetic characteristics of meson [31]. For instance, William et al [32] obtained bound state solutions of the radial Schrödinger equation by the combination of Hulthén and Hellmann potential within the framework of Nikiforov-Uvarov method. Also, Edet et al [33] obtained an approximate solution of the SE for the modified Kratzer potential plus screened Coulomb potential model using the Nikiforov-Uvarov method.…”

“…In this present work, we aim to study the SE with the combination of Hulthén and Hellmann potential analytically by using the NU method and apply the results to calculate the mass spectra of heavy quarkonium particles such as bottomonium and charmonium, in which the quarks are considered as spinless particles for easiness, which have not been considered before using this potentials to the best of our knowledge. The adopted potential is of the form [32] V…”

Analytical Investigation of the Single-Particle Energy Spectrum in Magic Nuclei of ⁵⁶Ni and ¹¹⁶Sn

“…To get the solution of (18), we need another change of variable with: To deal with the centrifugal barrier, we introduce the Greene-Aldrich approximation scheme [45]- [47] to analytically solve the equation. This approximation scheme is an excellent approximation to the centrifugal term, which is valid for By using (19), (20), and the change of variable in (19), the Schrodinger equation reads…”

Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

“…Also, Edet et al [34] obtained any-state solutions of the SE interacting with Hellmann-Kratzer potential model. William et al [35] obtained bound state solutions of the radial SE by the combination of Hulthén and Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for any arbitrarystate, with the Greene-Aldrish approximation in the centrifugal term. Inyang et al [36] studied any-state solutions of the SE interacting with class of Yukawa-Eckart potentials within the framework of NU method.…”