Improved energy spectra of the deformed Klein-Gordon and Schrödinger equations under the improved Varshni plus modified Kratzer potential model in the 3D-ERQM and 3D-ENRQM symmetries

• Published in: Indian journal of physics Vol. 97; no. 12; pp. 3567 - 3579
• Main Author: Maireche, Abdelmadjid
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2023; Springer Nature B.V
• Subjects: Antiparticles; Astrophysics and Astroparticles; Coupling (molecular); Diatomic molecules; Eigenvalues; Energy spectra; Mass spectra; Mathematical models; Mesons; Original Paper; Parameters; Perturbation theory; Physics; Physics and Astronomy; Quantum mechanics; Quantum numbers; Quantum physics; Relativistic effects; Schrodinger equation; Three dimensional models; Varshni plus modified Kratzer potential; Noncommutative quantum mechanics; Klien-Gordon equation; Schrödinger equation; Heavy-light mesons
• ISSN: 0973-1458; 0974-9845
• DOI: 10.1007/s12648-023-02681-4

The relativistic treatment of the improved Varshni plus modified Kratzer potential (IVMKP) models in the presence of some induced fields is carried out using the parametric Bopp's shift method and standard perturbation theory in the three-dimensional extended relativistic quantum mechanics (3D-ERQM) symmetries. The Varshni plus modified Kratzer potential (VMKP) model, as well as a combination of radial terms ( 1 1 - s 4 , s 1 - s 2 , s 1 - s 3 and 1 1 - s 3 ), which are coupled with the coupling L Θ , explains the interaction of the physical features of the system with the topological deformations of space-space. The new relativistic energy eigenvalues for diatomic molecules, such as (N 2 , CO, NO, I 2, and H 2 ) and bosonic particles and antiparticles under the IVMKP model have been derived using the principle of physical superposition. Quantum numbers ( j , l , s , m ), the mixed potential depths ( V 0 , S 0 ), the dissociation parameter D e and the equilibrium bond length r e , the screening parameter's inverse α and noncommutativity parameters Θ , τ , χ seemed to affect the new values we obtained. Within the framework of 3D-ERQM symmetries, we have treated certain significant particular instances that we hope will be valuable to the specialized researcher such as the improved Varshni potential and the improved modified Kratzer potential. The formulation of total energy was also discovered in the context of extended symmetries, which unified the energies of bosonic particles and antiparticles into a single mathematical formula. We have also treated the nonrelativistic limit and we apply our obtained results to generate the mass spectra of heavy-light mesons HLM, such as c c ¯ and b b ¯ under the IVMKP in the three-dimensional extended nonrelativistic quantum mechanics (3D-ENRQM) symmetries. When the three simultaneous limits of Θ , τ , χ vanished, we recovered the known relativistic results in the literature for Varshni plus modified Kratzer potential models.