Using the supersymmetric quantum mechanics (SUSY) approach, we obtained analytical approximate solutions to the Dirac equation with an improved Tietz diatomic potential function under spin and pseudospin symmetries. The energy eigenvalues equation and the corresponding wave spinor for the two symmetries have been explicitly obtained. The non relativistic limit of the spin symmetry has been obtained. The solution of Morse, Deng-Fan, and Rosen-Morse were obtained by changing the numerical value of q We have also obtained the thermodynamic properties of a system under the improved Tietz potential function.
The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.