Noncommutative of Klein–Gordon and Schrödinger equations in the background of the improved Hua plus modified Eckart potential model in 3D-(R/NR)NCQS symmetries: Spectrum and thermodynamic properties.

The impact of deformation space on the physical characteristics of diverse physics systems has been thoroughly investigated in research papers. In this work, we study the deformed Klein–Gordon equation (DKGE) in the three-dimensional relativistic non-commutative quantum space (3D-RNCQS) regime by using the improved Hua plus modified Eckart potential (IHPMEP) model. For this consideration, the DKGE in the 3D-RNCQS regime is solved using the standard perturbation theory and the well-known Bopp’s shifts method with the Greene–Aldrich approximation to the centrifugal barrier. The new relativistic energy equation and eigenfunction for the IHPMEP in the presence of deformation space-space for the heterogeneous (CO, HF, and NO) and homogeneous (N2, H2, and Li2) diatomic molecules are obtained to be sensitive to the atomic quantum numbers (j,l,s, and m), the mixed potential depths (V0,V1,V2, and V3), the inverse of the screening parameter α, and non-commutativity parameters (Φ, χ, and ζ). Analysis is performed on the non-relativistic limit of new energy spectra. By appropriately adjusting the combined potential parameters, we analyze the obtained new bound state eigenvalues of the DKGE and deformed Schrödinger equation with the IHPMEP in 3D-NCQS symmetries and obtain the new modified Eckart potential, the modified Hua potential, the modified Morse potential, and the modified Pöschl–Teller potential. Within the framework of the 3D-NRNCQS regime, the homogeneous and heterogeneous composite systems under IHPMEP models are examined. A thorough investigation is carried out into the impact of space-space deformation on the thermal parameters of the IHPMEP, including the partition function, mean energy, free energy, specific heat, and entropy. This work is of a fundamental absorbability nature and pedagogical interest in atomic and molecular physics. [ABSTRACT FROM AUTHOR]