Complete solutions of the Schrödinger equation with improved exponential Kratzer–Feus potential

This study rigorously investigates the improved exponential Kratzer–Feus potential (IEKFP) model combined with exponential Kratzer–Feus potential (EKFP) and other terms produced by the effect of phase–space deformation [Formula: see text]. The new energy equation in three-dimensional non-relativistic non-commutative phase–space (3D(NR-NCPS)) symmetries is obtained using the parametric generalized Bopp’s shifts method and standard independent time perturbation theory of hydrogen-related molecules (CH, H 2 , NO, HCL, and LiH) diatomic molecules. This is achieved by applying a Green–Aldrich approximation scheme to the centrifugal terms. The new non-relativistic energy equation for the IEKFP in the presence of deformation phase–space is dependent on the discrete atomic quantum numbers ([Formula: see text] and [Formula: see text], the dissociation energy [Formula: see text], the equilibrium bond length [Formula: see text], the screening parameter [Formula: see text], and the deformation phase–space parameters ([Formula: see text]. The new resulting energy equation is utilized to calculate 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 3D(NR-QM) and (3D(NR-NCPS)) symmetries. This study has multiple applications in various domains, including atomic and molecular physics. We have indicated that our work deals with the study of the possibility of the effect of various phase–space deformations on various physical values such as energy and various thermodynamic properties under the influence of exponential Kratzer–Feus potential. So we completed the study of Amadi et al.