Spin and pseudospin solutions to Dirac equation and its thermodynamic properties using hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential

Abstract

In this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.

Dirac equation and thermodynamic properties with the Modified Kratzer potential

“…A similar trend is observed for energy variation with quantum number, l. This is consistent with the results in Table 3 (see Figure 3). Figures 4,5,6,7,8,9,10,11,12, and 13 are plots showing variations of various thermodynamic properties of the diatomic molecules with the temperature parameter, β, and the upper bound vibrational quantum number, λ. In Figure 4, the partition function, Z, increases as β increases for the Cl 2 molecule, but decreases for the N 2 molecule.…”

“…The significance of spin and pseudospin symmetries in Dirac equation and their contributions in nuclear and Hadron physics is worthy of note [ 1 , 2 , 3 , 4 ]. As a result, some authors have discussed Dirac equation under various interactions [ 5 , 6 , 7 , 8 , 9 , 10 ].…”

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

“…The Greene-Aldrich approximation scheme is mostly applicable for short range potentials [7]. Eigensolutions for both relativistic and nonrelativistic wave equations have been studied with different methods which include the following: Exact quantisation, WKB, Nikiforov-Uvarov method (NU), Laplace transform technique, asymptotic iteration method, proper quantisation, supersymmetric quantum mechanics approach, vibrational approach, formula method, factorisation method, and Shifted 1/N-expansion method [8][9][10][11][12][13]. Bound state solutions obtained from the Schrödinger equation has practical applications in investigating tunnelling rate of quantum mechanical systems [14] and mass spectra of quarkonia systems [15][16][17][18][19].…”

Masses and thermal properties of a Charmonium and Bottomonium Mesons

“…Cao et al, [56], studied the TPs of light mesons, including the temperature dependence of their masses by solving the spatial correlation. In recent times scholars, have proposed new potentials through the combination of two potentials [57,58]. It's observed that the combination of at least two potential models has a propensity to fit experimental data more than a single potential [55].…”