arXiv subjects

V. H. Badalov

Publications and source records attributed to V. H. Badalov.

7 recordsLinked to original sources

arXiv2025

Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra

In this study, we present an analytical solution of the Dirac equation in a generalized tanh-shape hyperbolic potential, which allows us to unify various well-known quantum potentials under a single theoretical framework. This versatile potential model is used to compute the mass spectra for charmonium and bottomonium, with excellent agreement with experimental measurements and does better than some potential models in predicting the several orbital states. Our results not only validate the GTHP as a powerful tool for describing heavy quarkonium systems but also suggest its broader applicability in exploring quantum systems where similar potentials are effective. This work is a stepping stone for new research into fermionic systems with complex interactions, by jointly providing insights into foundational aspects of quantum mechanics as well as applications in particle physics.

hep-ph↗

arXiv2021

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.

hep-ph↗

arXiv2018

The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential

In this work, the analytical solutions of the $D$-dimensional Schrödinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential $V_{0}$, the radial $n_{r}$ and orbital $l$ quantum numbers and parameters $D, a, R_{0}$ are defined as well.

quant-ph↗

arXiv2017

Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential

In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well $V_{0}$ and $W$, the radial $n_{r}$ and $l$ orbital quantum numbers and parameters $D,a,R_{0}$ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a $^{56} Fe$ nucleus are calculated in $D=2$ and $D=3$, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of $D=2$ and $D=3$.

nucl-th↗

arXiv2011

Analytical solutions of the $D$-dimensional Schrödinger equation with the Woods-Saxon potential for arbitrary $l$ state

In this work, the analytical solution of the hyper-radial Schrödinger equation for the spherical Woods-Saxon potential in D dimensions 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.

math-ph↗

arXiv2011

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.

math-ph↗

arXiv2009

Analytical solutions of the Schrödinger equation with the Woods-Saxon potential for arbitrary $l$ state

In this work, the analytical solution of the radial Schrödinger 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.

math-ph↗