Analysis of the relativistic and non-relativistic non-commutative quantum systems subject to improved inversely quadratic Hellmann potential model in 3D-(R/NR) NCQS symmetries
Keywords:
Klein-Gordon equation; Dirac equation; Schrödinger equation; Inversely quadratic Hellman; Non-commutative space.Abstract
: We present an improved inversely quadratic Hellman (IIQHP) model and determine its new eigenvalue solutions in the context of three-dimensional relativistic/non-relativistic non-commutative quantum mechanics (3D-(R/NR) NCQS). The parametric Bopp's shifts approach and standard perturbation theory are used in the frameworks of the 3D-(R/NR) NCQS to examine the novel high and lower energy spectrum within deformed Dira, Klein-Gordon, and Shrodinger regimes for IIQHP. We obtained new eigensolutions for the bosonic particles (spin-0, 1,...), fermionic particles with spin and p-spin symmetry with (spin/p-spin)-1/2 to be sensitive to the atomic quantum numbers ( ), the mixed potential depths ( ), the screening parameter and the disctet deformation parameters ( ). We recovered many potentials in the deformed Dirac equation, the deformed Klein-Gordon equation, and the deformed Schrodinger equation, including the newly modified Coulomb potential and the modified inversely quadratic Yukawa potential. The new non-relativistic eigenvalue solution of MYKP is then applied to obtain the spin-averaged mass spectra of the heavy mesons such, eg. and . To complete this study, we also explore the new partition function for the IIQHP, which is determined as a function of the corresponding partition function for IQHP potentials and non-commutativity parameters ( ). Other thermodynamic properties, such as new mean energy , new mean free energy , new entropy , and new heat capacity are determined for the IIQHP in the context of the deformed Schrodinger equation. We highlight that our results are consistent with the previous works presented in the literature when the simultaneous limits are achieved, which indicates ignoring the deformation of the space-space.
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