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Abstract

Using two physical models, we investigate the three-dimensional deformed Schrödinger equation (3D-DSE) in the context of three-dimensional non-relativistic noncommutative quantum phase-space (3D(NR)-NCPS) symmetries. The Mobius square potential is what they have in common. The first is the improved modified Mobius square plus Eckart potential (IMMSEPM), and the second is the improved Mobius square plus screened-Kratzer potential (IMSSKPM). This study solves the 3D-DSE in the 3D(NR)-NCPS regime using the well-known generalized Bopp’s shifts method and conventional perturbation theory. For the homogeneous (K2 and H2) and heterogeneous (LiH, HCl, HF, DF, and CsO) diatomic molecules, the new non-relativistic energies equations and eigenfunction for the IMMSEPM and the IMSSKPM models in the presence of deformation phase-space are obtained to be sensitive to the atomic quantum numbers (j, l, s, m), the mixed potential depths (V0, V1, V2, A, B) and (A, B, De, re), the screening parameter α, and non-commutativity parameters (Θ/Φ, χ/χ, ζ/ζ) for the IMMSEPM and the IMSSKPM, respectively. By appropriately adjusting the improved modified Mobius square potential, the improved Eckart potential, the improved Hulth'{e}n potential, and the improved Poschl-Teller potential, we investigate the obtained new bound state eigenvalues of the DSE with the IMMSEPM and the IMSSKPM in 3D(NR)-NCPS symmetries. In addition, the partition function, mean energy, free energy, specific heat, and entropy of the IMMSEPM and IMSSKPM are investigated in 3D(NR)-NCPS symmetries. The current research has many potential applications in atomic and molecular physics.

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