Bound state solutions of the Dirac equation for the generalized Cornell potential model

In this study, the bound state solutions of the Dirac equation (DE) have been determined with the generalized Cornell potential model (GCPM) under the condition of spin symmetry. The GCPM includes the Cornell potential plus a combination of the harmonic and inversely quadratic potentials. In the framework of the Nikiforov–Uvarov (NU) method, the relativistic and nonrelativistic energy eigenvalues for the GCPM have been obtained. The energies spectra of the Kratzer potential (KP) and the modified Kratzer potential (MKP) have been derived as particular cases of the GCPM. The present results have been applied to some diatomic molecules (DMs) as well as heavy and heavy-light mesons. The energy eigenvalues of the KP and MKP have been computed for several DMs, and they are fully consistent with the results found in the literature. In addition, the energy eigenvalues of the GCPM have been employed for predicting the spin-averaged mass spectra of heavy and heavy-light mesons. One can note that our predictions are in close agreement with the experimental data as well as enhanced compared to the recent studies.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

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.

Holographic anisotropic model for light quarks with confinement-deconfinement phase transition

We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.

Aharonov–Bohm effect on the generalized Duffin–Kemmer–Petiau oscillator in the Som–Raychaudhuri spacetime

The generalized Duffin–Kemmer–Petiau (DKP) oscillator with electromagnetic interactions in the curved spacetimes is investigated. We introduce firstly the generalized DKP oscillator in Som–Raychaudhuri spacetime with Cornell potential. Then, we consider the electromagnetic interactions into the generalized DKP oscillator. The energy eigenvalues and eigenfunction of our problem are obtained. The effects from the parameters of spacetime, the frequency of oscillator, the Cornell potential and the magnetic flux on the energy eigenvalues have been analyzed. We find an analog effect for the bound states from the Aharonov–Bohm effect in our considered system.

Confining potential under the gauge field condensation in the SU(2) Yang-Mills theory

QǬ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci-Ferrari type, the possibility of a gluon condensation ⟨Aμ+ Aμ−⟩ in low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales rc and ˜R0. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.

The generalized Klein–Gordon oscillator with position-dependent mass in a particular Gödel-type space–time

The relativistic quantum dynamics of the generalized Klein–Gordon (KG) oscillator having position-dependent mass in the Gödel-type space–time is investigated. We have presented the generalized KG oscillator in this space–time, and discussed the effect of Cornell potential and linear potential for our considered system. The modification from the parameters of position-dependent mass and characterizing the space–time for the energy spectrums are presented.

The study of the generalized boson oscillator in a chiral conical space–time

Our work mainly study the relativistic generalized boson oscillator namely generalized Duffin–Kemmer–Petiau (DKP) oscillator with the function [Formula: see text] considered as the Cornell potential under the chiral conical space–time background. We obtain the wave function and energy spectrum of radial equation by using commonly used the Nikiforov–Uvarov method. It is shows that the energy spectrum of the generalized DKP oscillator depend explicitly on the angular deficit [Formula: see text], related rotation parameter [Formula: see text] and torsion parameter [Formula: see text], which characterize the global structure of the metric in the chiral conical space–time. In addition, the Cornell potential parameters [Formula: see text] have non-negligible influence on the energy spectrum of the studied systems.