Within the framework of non-relativistic non-commutative phase–space, the new bound state approximate solution of the deformed Schrödinger equation is solved for the improved screened modified Kratzer and a class of Yukawa potential (ISMK-CYP) models using the GBSM and standard perturbation theory. By employing the Greene–Aldrich-type approximation scheme, we have obtained the new explicit energy eigenvalues for the newly proposed ISMK-CYP for the homogeneous (I \(_{2}\) , N \(_{2}\) ) and heterogeneous (Hcl, ScH, LiH, CO, NO, and CH) diatomic molecules and the heavy mesons system such as \(c {\overline{c}}\) and \(b{\overline{b}}\) . Our new results show that the bound state energy is highly sensitive to the atomic quantum numbers ( \(j,l,s,\ \) and m), the mixed potential depths ( \(a,b,c,f,\ \ \) and g), the screening parameter \( \phi _{a}\) , and non-commutativity parameters \(\left( \Phi ,\chi ,\zeta \right) \) and \(\left( \eta ,{\overline{\chi }},{\overline{\zeta }}\right) \) . We examine the obtained new bound state eigenvalues of the DSE with the IIQH-KP in 3D-NRNCQPS symmetries by suitable adjustment of the combined potential parameters and get the improved screened modified Kratzer model and the improved class of Yukawa potential model. The influence of the deformation of phase–space on the spin-averaged mass spectra of the heavy–light mesons such as \(c{\overline{c}}\) and \(b{\overline{b}}\) under the ISMK-CYP model in 3D-NRNCQPS symmetries was investigated. The vibrational partition function, vibrational mean energy, vibrational mean free energy, vibrational entropy, and vibrational specific heat capacity are among the novel thermodynamic parameters that are evaluated as well. The current study has several applications in various areas, including atomic and molecular physics.
