394 research outputs found
Solutions of the spatially-dependent mass Dirac equation with the spin and pseudo-spin symmetry for the Coulomb-like potential
We study the effect of spatially dependent mass function over the solution of
the Dirac equation with the Coulomb potential in the (3+1)-dimensions for any
arbitrary spin-orbit state In the framework of the spin and
pseudospin symmetry concept, the analytic bound state energy eigenvalues and
the corresponding upper and lower two-component spinors of the two Dirac
particles are obtained by means of the Nikiforov-Uvarov method, in closed form.
This physical choice of the mass function leads to an exact analytical solution
for the pseudospin part of the Dirac equation. The special cases ( i.e., s-wave) the constant mass and the
non-relativistic limits are briefly investigated.Comment: 24 page
Approximate Analytical Solutions of the Effective Mass Dirac Equation for the generalized Hulthen Potential with any kappa-Value
The Dirac equation, with position-dependent mass, is solved approximately for
the generalized Hulth\'{e}n potential with any spin-orbit quantum number
. Solutions are obtained by using an appropriate coordinate
transformation, reducing the effective mass Dirac equation to a
Schr\"{o}dinger-like differential equation. The Nikiforov-Uvarov method is used
in the calculations to obtain energy eigenvalues and the corresponding wave
functions. Numerical results are compared with those given in the literature.
Analytical results are also obtained for the case of constant mass and the
results are in good agreement with the literature.Comment: 13 page
Effective Mass Dirac-Morse Problem with any kappa-value
The Dirac-Morse problem are investigated within the framework of an
approximation to the term proportional to in the view of the
position-dependent mass formalism. The energy eigenvalues and corresponding
wave functions are obtained by using the parametric generalization of the
Nikiforov-Uvarov method for any -value. It is also studied the
approximate energy eigenvalues, and corresponding wave functions in the case of
the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page
Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem
The role of the Hulthen potential on the spin and pseudospin symmetry
solutions is investigated systematically by solving the Dirac equation with
attractive scalar S(r) and repulsive vector V(r) potentials. The spin and
pseudospin symmetry along with orbital dependency (pseudospin-orbit and
spin-orbit dependent couplings) of the Dirac equation are included to the
solution by introducing the Hulthen-square approximation. This effective
approach is based on forming the spin and pseudo-centrifugal kinetic energy
term from the square of the Hulthen potential. The analytical solutions of the
Dirac equation for the Hulthen potential with the spin-orbit and
pseudospin-orbit-dependent couplings are obtained by using the Nikiforov-Uvarov
(NU) method. The energy eigenvalue equations and wave functions for various
degenerate states are presented for several spin-orbital, pseudospin-orbital
and radial quantum numbers under the condition of the spin and pseudospin
symmetry. Keywords: Spin and pseudospin symmetry; orbital dependency; Dirac
equation; Hulthen potential; Nikiforov-Uvarov Method.Comment: 14 pages and 3 figure
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