Analytical solutions of the Schr\"{o}dinger equation with the Woods-Saxon potential for arbitrary ll state

In this work, the analytical solution of the radial Schr\"{o}dinger equation for the Woods-Saxon potential is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary $l$ states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of $n$ and $l$ quantum numbers.Comment: 14 page

Dissociation of Quarkonium in hot and Dense Media in an Anisotropic Plasma in the Non-Relativistic Quark Model

In this paper, quarkonium dissociation is investigated in an anisotropic plasma in the hot and dense media. For that purpose, the multidimensional Schrodinger equation is solved analytically by Nikiforov-Uvarov (NU) method for the real part of the potential in an anisotropic medium. The binding energy and dissociation temperature are calculated. In comparison with an isotropic medium, the binding energy of quarkonium is enhanced in the presence of an anisotropic medium. The present results show that the dissociation temperature increases with increasing anisotropic parameter for 1S state of the charmonium and bottomonium. We observe that the lower baryonic chemical potential has small effect in both isotropic and anisotropic media. A comparison is presented with other pervious theoretical works.Comment: 11 pages, 10 figures, 1 table

Any l-state analytical solutions of the Klein-Gordon equation for the Woods-Saxon potential

The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any $l$ states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers $n$ and $l$. The non-relativistic limit of the bound state energy spectrum was also found.Comment: 15 pages, 1 tabl

Spectra of Heavy Quarkonia in a Magnetized-Hot Medium in the Framework of Fractional Non-relativistic Quark Model

In the fractional nonrelativistic potential model, the decomposition of heavy quarkonium in a hot magnetized medium is investigated. The analytical solution of the fractional radial Schrodinger equation for the hot-magnetized interaction potential is displayed by using the conformable fractional Nikiforov-Uvarov method. Analytical expressions for the energy eigenvalues and the radial wave function are obtained for arbitrary quantum numbers. Next, we study the charmonium and bottmonium binding energies for different magnetic field values in the thermal medium. The effect of the fractional parameter on the decomposition temperature is also analyzed for charmonium and bottomonium in the presence of hot magnetized media. We conclude that the dissociation of heavy quarkonium in the fractional nonrelativistic potential model is more practical than the classical nonrelativistic potential model.Comment: 13 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2104.0054