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- Title
The investigation of approximate solutions of Deformed Klein-Fock-Gordon and Schrödinger Equations under Modified Equal Scalar and Vector Manning-Rosen and Yukawa Potentials by using the Improved Approximation of the Centrifugal term and Bopp's shift Method in NCQM Symmetries
- Authors
Maireche, Abdelmadjid
- Abstract
In the current work, we employed the elegant tool of Bopp's shift and standard perturbation theory methods to obtain a new relativistic and nonrelativistic approximate bound state solution of deformed Klein-Fock-Gordon and deformed Schrödinger equations using the modified equal vector scalar Manning-Rosen potential and Yukawa potential model. Furthermore, we have employed the improved approximation to the centrifugal term for some selected diatomic molecules such as (N2, I2, HCl, CH and LiH) in the symmetries of extended quantum mechanics to obtain the approximate solutions. It is seen that relativistic shift energy ΔEmytot (Θ, σ, Χ, n, j, l, s, m) and the perturbative nonrelativistic corrections ΔEmyNR (Θ, σ, b, A, α, V0, n, j, l, s, m) are sensitive to the quantum numbers (n, j, l, s, m), the potential range b, two dimensionless parameters (A and α), the strength of the potential V0 in addition to the parameters of noncommutativity (Θ, σ, χ). We have highlighted three physical phenomena that automatically generate a result of the topological properties of noncommutativity, the first generated physical phenomena are the perturbative spin-orbit coupling, the second the magnetic induction while the third corresponds to the rotational proper phenomena. In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of quantum field theory and quantum mechanics. A straightforward limit of our results to ordinary quantum mechanics shows that the present result under modified equal vector scalar Manning-Rosen potential and Yukawa potential is consistent with what is obtained in the literature. In the new symmetries of NCQM, is not possible to get the exact analytical solutions for l = 0 and l ≠ 0, the approximate solutions are available. We have observed that the deformed Klein-Fock-Gordon equation under the modified equal vector scalar Manning-Rosen potential and Yukawa potential model has a physical behavior similar to the Duffin-Kemmer equation for meson with spin-1, it can describe a dynamic state of a particle with spin-1 in the symmetries of RNCQM. The NRNCQM and RNCQM results obtained within Bopp's shift and standard perturbation theory methods overlap entirely with the results obtained by ordinary NCQM, and it displays that the theoretical investigation in this study is excellent.
- Subjects
KLEIN-Gordon equation; PERTURBATION theory; SCHRODINGER equation
- Publication
Latin-American Journal of Physics Education, 2021, Vol 15, Issue 2, p1
- ISSN
1870-9095
- Publication type
Article