Arbitrary Solution of the Schrödinger Equation Interacting with the Superposition of Hulthen with Spin-orbit Plus Adjusted Coulomb Potential Model

In this study, we solve the non-relativistic radial part of the Schrödinger wave equation for the superposition of the Hulthen with spin-orbit plus adjusted Coulomb potential (SHSC) potential using the Nikiforov-Uvarov (NU) method for arbitrary states. The Hulthen with spin-orbit plus adjusted Coulomb (SHSC) potential is the simplest potential field for a nuclear system and has been used to obtain the single particle energy spectrum for both nucleon species orbiting a closed nuclear core. We also obtained in this study the corresponding single particle normalized wave function expressed in terms of the Jacobi polynomial. Besides, we obtained two special cases of the energy spectra for the SHSC potential.

Non-relativistic Quark Model under External Magnetic and Aharanov-Bohm (AB) Fields in the Presence of Temperature-Dependent Confined Cornell Potential

The dissociation of quarkonia in a thermal QCD medium in the background of an AB and strong magnetic fields is investigated. For this purpose, the Schrödinger equation with a charged quarkonium in the Cornell potential under the influence of AB flux and an external magnetic fields directed along the z-axis is employed. By using the Nikiforov-Uvarov (NU) method, the energy eigenvalue is obtained. The effect of temperature, AB flux, and an external magnetic field is studied. The study shows that the dissociation energy of 1S states of charmonium and bottomonium decreases with increasing temperature and AB flux, and external magnetic field. Also, the quarkonium melts faster in a hot medium in the presence of AB flux and external magnetic field. We found that the charmonium melts at 13.79 m²_πGeV² and the bottomonium melts at 99.48 m²_πGeV² . A comparison is studied with other works. Thus, the present non-relativistic model gives satisfactory results for dissociation binding energy in a hot medium when AB flux and external magnetic fields are included.

Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra.

Spin Splitting Spectroscopy of Heavy Quark and Antiquarks Systems

Phenomenological potentials describe the quarkonium systems like c c ¯ , b b , ¯ and b ¯ c where they give a good accuracy for the mass spectra. In the present work, we extend one of our previous works in the central case by adding spin-dependent terms to allow for relativistic corrections. By using such terms, we get better accuracy than previous theoretical calculations. In the present work, the mass spectra of the bound states of heavy quarks c c ¯ , b b ¯ , and 𝐵𝑐 mesons are studied within the framework of the nonrelativistic Schrödinger equation. First, we solve Schrödinger’s equation by Nikiforov-Uvarov (NU) method. The energy eigenvalues are presented using our new potential. The results obtained are in good agreement with the experimental data and are better than the previous theoretical estimates.

Melting of quarkonium in an anisotropic hot QCD medium in the presence of a generalized Debye screening mass and Nikiforov–Uvarov’s method

Generalized temperature and anisotropy dependent Debye screening mass is introduced into the real part of a potential in an anisotropic plasma. The N-radial Schrödinger equation (SE) is approximately solved by using the Nikiforov–Uvarov (NU) method which based on the expansion of power series. Binding energies and dissociation temperatures of charmonium and bottomonium are calculated. In addition, we have calculated the screening mass values for different parameters. Comparing to their values in an isotropic medium, the charmonium and bottomonium binding energies within an anisotropic medium are found to be increased. Also, the dissociation temperatures of both the charmonium and the bottomonium within anisotropic environments appear larger relative to those found within an isotropic medium. Finally, one observes that in any medium the bottomonium dissociation temperature is higher than the charmonium one.

Solving of the Schrodinger equation analytically with an approximated scheme of the Woods–Saxon potential by the systematical method of Nikiforov–Uvarov

The analytic solutions of the Schrodinger equation for the Woods–Saxon (WS) potential and also for the generalized WS potential are obtained for the [Formula: see text]-wave nonrelativistic spectrum, with an approximated form of the WS potential and centrifugal term. Due to this fact that the potential is an exponential type and the centrifugal is a radial term, we have to use an approximated scheme. First, the Nikiforov–Uvarov (NU) method is introduced in brief, which is a systematical method, and then Schrodinger equation is solved analytically. Energy eigenvalues and the corresponding eigenvector are derived analytically by using the NU method. After that, the generalized WS potential is discussed at the end.

Bound State Solutions of Three-Dimensional Klein-Gordon Equation for Two Model Potentials by NU Method

In this study, we investigate the relativistic Klein-Gordon equation analytically for the Deng-Fan potential and Hulthen plus Eckart potential under the equal vector and scalar potential conditions. Accordingly, we obtain the energy eigenvalues of the molecular systems in different states as well as the normalized wave function in terms of the generalized Laguerre polynomials function through the NU method, which is an effective method for the exact solution of second-order linear differential equations.

Calculation of the energy levels and charge radius of 24Mg and 32S isotopes in the cluster model

In this work, the 24Mg and 32S isotopes are considered in the cluster model by solving the Schrödinger and Klein–Gordon equations using the Nikiforov–Uvarov (NU) method. The configuration of the alpha particles for the second excited state for 24Mg isotope is 12C + 12C. A local potential is used for these two equations that is compatible to the modified Hulthen plus quadratic Yukawa potential. By substituting this potential in the Schrödinger and Klein–Gordon equations, the energy levels and wave functions are obtained. The calculated results from the Schrödinger and Klein–Gordon equations, i.e., nonrelativity and relativity, respectively, are close to the results from experimental data.

Relativistic treatment of the Hellmann-generalized morse potential

We present the relativistic treatment of the Hellmann-generalized Morse potential using Nikiforov-Uvarov(NU) method. The relativistic equations(Klein-Gordon and Dirac equation) were solved using the conventional NU method. In order to overcome the centrifugal barrier, we employed the well-known Greene and Aldrich approximation scheme. The corresponding normalized eigenfunctions was also obtained in each case. It was shown that in the non-relativistic limits, both energy equations obtained by solving Klein-Gordon and Dirac equations, and wavefunctions reduced to the non-relativisitc energy Equation. The bound state energy eigenvalues for N2, CO, NO, CH and HCl diatomic molecules were computed for various vibrational and rotational quantum numbers. It was found that our results agree with those in literature.