Journal Title, Volume, Page:

Journal of Modern Physics, 3, 170-179
Year of Publication:

2012
Preferred Abstract (Original):

In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by the Nikiforov-Uvarov (NU) method, in a closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.

Journal Title, Volume, Page:

Applied Mathematics and Computation, Volume 217, Issue 22, 9019–9032
Year of Publication:

2011
Preferred Abstract (Original):

The role of the Hulthén potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar and repulsive vector 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 Hulthén-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthén potential. The analytical solutions of the Dirac equation for the Hulthén 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.

Journal Title, Volume, Page:

Volume 216, Issue 3, Pages 911–923
Year of Publication:

2010
Preferred Abstract (Original):

We solve the Dirac equation approximately for the attractive scalar *S*(*r*) and repulsive vector *V*(*r*) Hulthén potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number *κ*.
In the framework of the spin and pseudospin symmetric concept, we
obtain the analytic energy spectrum and the corresponding two-component
upper- and lower-spinors of the two Dirac particles by means of the
Nikiforov–Uvarov method in closed form. The limit of zero tensor
coupling and the non-relativistic solution are obtained. The energy
spectrum for various levels is presented for several *κ* values under the condition of exact spin symmetry in the presence or absence of tensor coupling.

Journal Title, Volume, Page:

Volume 218, Issue 20 , Pages 10082–10093
Year of Publication:

2012
Preferred Abstract (Original):

The approximate analytical solutions of the Dirac
equations with the reflectionless-type and Rosen–Morse potentials
including the spin–orbit centrifugal (pseudo-centrifugal) term are
obtained. Under the conditions of spin and pseudospin (pspin) symmetry
concept, we obtain the bound state energy spectra and the corresponding
two-component upper- and lower-spinors of the two Dirac particles by
means of the Nikiforov–Uvarov (NU) method in closed form. The special
cases of the *s*-wave Dirac equation and the non-relativistic limit of Dirac equation are briefly studied.

Journal Title, Volume, Page:

Journal of Physics A Mathematical and Theoretical, 44(35):355301
Year of Publication:

2011
Preferred Abstract (Original):

The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthén potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov–Uvarov method is used in the calculations. The orbital dependence (spin–orbit- and pseudospin–orbit-dependent coupling too singular 1/r2) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.