On the deformed Dirac equation for the improved quadratic
exponential-type potential plus Eckart potential including the
Yukawa-like tensor interaction at the noncommutative framework
Abstract
In this manuscript, we present a generalized formulation of the deformed
Dirac equation, by considering the effect of a noncommutative space-time
on the improved quadratic exponential-type potential plus Eckart
potential and Yukawa-like tensor interaction (IQEPEP-YTi, in short).
Using the Bopp’s shift method arising from the Weyl-Moyal star product,
we obtain modified DDE equations for spin and p-spin symmetries. The new
values of energy that we got appeared sensitive to the quantum numbers
(j,k,s,l,m,…), the mixed potential depths (a,b,c,A,B), the range
of the potential , and noncommutativity parameters . The three physical
phenomena that are automatically generated as a result of the
topological properties of noncommutativity are the perturbative
spin-orbit coupling, the magnetic induction, and the third corresponds
to the rotational proper phenomena. We show that the corrections to the
spectrum energy are smaller than the main energy in the usual cases of
the Dirac equation. The three physical phenomena that are automatically
generated as a result of the topological properties of noncommutativity
are the perturbative spin-orbit coupling, the magnetic induction, and
the third corresponds to the rotational proper phenomena. We show that
the corrections to the spectrum energy are smaller than the main energy
in the usual cases of quantum field theory. In the new symmetries of
extended relativistic quantum mechanics ERQM, it is not possible to get
the exact analytical solutions for k=0 and, only the approximate
solutions are available. Some special cases of our solution are
investigated by choosing appropriate parameters in the IQEPEP-YTi model.