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.
Hulthen plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the thermodynamic properties and the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmoniumand cc and bottomonium bb, and thermodynamic properties such as the mean energy, the specific heat, the free energy, and the entropy. Four special cases were considered when some of the potential parameters were set to zero, resulting in Hellmann potential, Yukawa potential, Coulomb potential, and Hulthen potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.
A class of Yukawa potential is adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. The potential was made to be temperature-dependent by replacing the screening parameter with Debye mass. We solved the radial Schrödinger equation analytically using the series expansion method and obtained the energy eigenvalues. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium and bottomonium . Two special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, and Coulomb potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.
The Schrödinger equation has been solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov-Uvarov-Functional Analysis (NUFA) method. The bound state energy and wave function for the HSKP have been obtained in closed form by applying the Greene-Aldrich approximation scheme to the inverse square term. Using the resulting energy equation, we computed the energy spectra for twelve diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H<sub>2</sub>, ScH, CO, I<sub>2</sub>, N<sub>2</sub>, and NO) for various quantum states. In order to show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.
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