arXiv subjects

S. V. Badalov

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

3 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

Analytical bound-state solutions of the Klein-Fock-Gordon equation for the sum of Hulthén and Yukawa potential within SUSY quantum mechanics

The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound-state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and non-equal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary $l$ states. Beyond that, a closed-form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The non-relativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

hep-th↗

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↗