Investigating the effects of phase-space non-commutativity coordinates on the modified Deng-Fan Yukawa potential model and thermodynamic properties in 3D(NR-NCPS) and 3D(NR-QM) symmetries

An approximate new bound state solution of the three-dimensional deformed Schrodinger equation under the deformed phase-space sym- ¨ metries for the modified Deng-Fan Yukawa potential model that is obtained from the combination of the corresponding expression in threedimensional non-relativistic quantum mechanics symmetries and some central terms [exp (−αr)/r (1 − exp (−αr)), exp (−2αr)/r (1 − exp (−αr))2 , exp (−3αr)/r (1 − exp (−αr))3 , exp (−αr)/r 2 , exp (−αr)/r 3 and 1/r 4 ] coupled with the infinitesimal non-commutativity vector Θ and the angular momentum operator L. With the help of the parametric generalized Bopp’s shifts method, the independent time perturbation theory method, and an approximation scheme, the analytical energies of the studied were obtained for both symmetries, for different quantum numbers. The new non-relativistic energy equation under the studied potential for the homogenous diatomic molecules (HODMs) (H2, I2); the heterogeneous diatomic molecules (CO, HCl, LiH); the neutral transition metal hydrides (ScH, TiH, VH, CrH); the transition-metal lithide (CuLi); the transition-metal carbides (TiC, NiC); the transition metal nitrite (ScN) and the transition metal fluoride (ScF) and in the presence of deformation phase-space are dependent on the discrete atomic quantum numbers (j, l, s and m), the dissociation energy, the equilibrium bond length, and the screening parameter (re, De, and α), the deformation phase parameters (P nc p and S nc p ). The new resulting energy equation is utilized to calculate spin-averaged mass spectra of the heavy mesons under the studied potential and Deng-Fan Yukawa potential model in three-dimensional non-relativistic quantum mechanics and 3it’s extended symmetries. Furthermore, we have calculated the partition function, from which thermodynamic properties such as mean energy, specific heat capacity, entropy, and free energy are derived in both three-dimensional non-relativistic quantum mechanics and the deformed phase-space symmetries symmetries. Notably, the two special cases, representing the modified Yukawa potential and the modified Deng-Fan potential were treated in extended phase-space symmetry for energies and thermodynamic properties. Our current study promises to apply to different areas of physics in various domains, including atomic and molecular physics.