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- Title
The investigation of approximate solutions of Deformed Schrödinger Equations for the Hydrogenic Atoms, Heavy Quarkonium Systems QQ̄(Q = b, c) and Diatomic molecule Bound-State Problem under Improved Exponential, Generalized, Anharmonic Cornell potential Model in NCPS symmetries
- Authors
Maireche, Abdelmadjid
- Abstract
Recently Ibekwe et al. (Ref [16]) have treated the bound state solution of the radial Schrödinger equation for the exponential generalized Cornell anharmonic potential (EGACp, in short, see Eq. (1)) model within the framework of quantum mechanics known in the literature. According to the generalized Bopp's shift method and standard perturbation theory, we generalize this process by adding multi-variable coupling potentials ... together with the EGACp model in three-dimensional nonrelativistic quantum mechanics noncommutative phase space (3DNRQm-NCPS) including the effect of the centrifugal term. The multi-variable coupling potentials appear as a result of the effects of NC properties of space and phase on the EGACp model. We called this newly proposed potential the improved generalized Cornell anharmonic potential (IEGACp, in short, see Eq. (2)) model. We were able to discover a new application of this potential to hydrogen atoms He+, Li+2, and Be+, in addition to other applications the heavy quarkonium systems (𝑐𝑐𝑐𝑐 and 𝑏𝑏𝑏𝑏) and some selected diatomic molecules (CO, NO, CH and N2) known in the literature within the framework of (3DNRQm-NCPS). The obtained energy is sensitive to discreet atomic quantum numbers (𝑗𝑗, 𝑛𝑛, 𝑙𝑙, 𝑠𝑠 and 𝑚𝑚), the noncommutativity parameter (𝛩𝛩, 𝜎𝜎, 𝜒𝜒) due to the topological properties of the self-quantum influence of space-space and phase-phase, in (3DNRQm-NCPS) symmetries, in addition to the discreet atomic quantum numbers (𝑛𝑛, 𝑙𝑙) and the parameters (𝑎𝑎, 𝑏𝑏, 𝑐𝑐, 𝑑𝑑, 𝑒𝑒, 𝑓𝑓, 𝛼𝛼) or (𝑟𝑟𝑒𝑒, 𝐷𝐷𝑒𝑒, 𝛼𝛼) of the EGACp model that appeared in the literature. Furthermore, we have shown that the corresponding Hamiltonian operator in (3DNRQm-NCPS) symmetry is the sum of the Hamiltonian operator of EGACp and three operators, the first one is the perturbed spin-orbit interaction, the second is the modified Zeeman operator while the last part corresponds to the induced rotational Fermi Hamiltonian. The new mass spectrum of the heavy quarkonium systems is carried out by introducing the IEGACp model in (3DNRQm-NCPS) symmetries. The comparison with other special cases of potentials in the literature is motivating. The limiting cases are analyzed for (𝛩𝛩, 𝜎𝜎, 𝜒𝜒) and (𝛩𝛩𝑐𝑐, 𝜎𝜎𝑐𝑐, 𝜒𝜒𝑐𝑐) → (0,0,0) and are compared with those of literature.
- Subjects
QUARKONIUMS; ATOMS
- Publication
Latin-American Journal of Physics Education, 2022, Vol 16, Issue 2, p1
- ISSN
1870-9095
- Publication type
Article