Journal Title, Volume, Page:

The European Physical Journal Plus , 129:1
Year of Publication:

2014
Preferred Abstract (Original):

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:

Journal of Mathematical Chemistry, Volume 51, Issue 1, pp 227-238
Year of Publication:

2013
Preferred Abstract (Original):

We obtain the bound-state solutions of the radial Schrödinger equation with the shifted Deng–Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary *l*-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

Journal Title, Volume, Page:

Chin. Phys. B Vol. 21, No. 11, 110302
Year of Publication:

2012
Preferred Abstract (Original):

We study the effects of the perpendicular magnetic and Aharonov-Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

Journal Title, Volume, Page:

Central European Journal of Physics , Volume 10, Issue 2, pp 361-381
Year of Publication:

2012
Preferred Abstract (Original):

Using an
approximation scheme to deal with the centrifugal (pseudo-centrifugal)
term, we solve the Dirac equation with the screened Coulomb (Yukawa)
potential for any arbitrary spin-orbit quantum number *κ*.
Based on the spin and pseudospin symmetry, analytic bound state energy
spectrum formulas and their corresponding upper- and lower-spinor
components of two Dirac particles are obtained using a shortcut of the
Nikiforov-Uvarov method. We find a wide range of permissible values for
the spin symmetry constant *C*
_{
s
} from the valence energy spectrum of particle and also for pseudospin symmetry constant *C*
_{
ps
} from the hole energy spectrum of
antiparticle. Further, we show that the present potential interaction
becomes less (more) attractive for a long (short) range screening
parameter *α*. To remove the degeneracies in
energy levels we consider the spin and pseudospin solution of Dirac
equation for Yukawa potential plus a centrifugal-like term. A few
special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa,
the Yukawa plus centrifugal-like potentials, the limit when *α*
becomes zero (Coulomb potential field) and the non-relativistic limit
of our solution are studied. The nonrelativistic solutions are compared
with those obtained by other methods.

Journal Title, Volume, Page:

Cent. Eur. J. Phys., 8(4), 652-666
Year of Publication:

2010
Preferred Abstract (Original):

We study the
approximate analytical solutions of the Dirac equation for the
generalized Woods-Saxon potential with the pseudo-centrifugal term. We
apply the Nikiforov-Uvarov method (which solves a second-order linear
differential equation by reducing it to a generalized hypergeometric
form) to spin- and pseudospin-symmetry to obtain, in closed form, the
approximately analytical bound state energy eigenvalues and the
corresponding upper- and lower-spinor components of two Dirac particles.
The special cases *κ* = ±1 (*s* =
= 0, *s*-wave)
and the non-relativistic limit can be reached easily and directly for
the generalized and standard Woods-Saxon potentials. We compare the
non-relativistic results with those obtained by others.

Journal Title, Volume, Page:

Chinese Physics C, Vol. 37, No. 6, 063101
Year of Publication:

2013
Preferred Abstract (Original):

By applying an appropriate Pekeris
approximation to deal with the centrifugal term, we present an
approximate systematic solution of the two-body spinless Salpeter (SS)
equation with the Woods-Saxon interaction potential for an arbitrary *l*-state.
The analytical semi-relativistic bound-state energy eigenvalues and the
corresponding wave functions are calculated. Two special cases from our
solution are studied: the approximated Schrödinger-Woods-Saxon problem
for an arbitrary *l*-state and the exact *s*-wave (*l*=0).

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.

Journal Title, Volume, Page:

Ann. Phys. (Berlin) 17, No. 11, 897 – 910
Year of Publication:

2008
Preferred Abstract (Original):

The Schrödinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The NikiforovUvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers n and l with three different values of the potential parameter α. It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional system from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation (n, l, D) → (n, l ±1,D∓2). This solution reduces to the Hulthén potential case.

Journal Title, Volume, Page:

Ann. Phys. (Leipzig) 16, No. 3, 218 – 232
Year of Publication:

2007
Preferred Abstract (Original):

The one-dimensional Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov(NU} method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.