Journal Title, Volume, Page:

Annals of Physics Volume 341, Pages 153–163
Year of Publication:

2014
Preferred Abstract (Original):

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.

Journal Title, Volume, Page:

Pramana , Volume 83, Issue 1, pp 49-61
Year of Publication:

2014
Preferred Abstract (Original):

Journal Title, Volume, Page:

Physica B: Condensed Matter Volume 407, Issue 21, 4198–4207
Year of Publication:

2012
Preferred Abstract (Original):

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.

Journal Title, Volume, Page:

Molecular Physics Vol. 110, No. 24 , 3031–3039
Year of Publication:

2012
Preferred Abstract (Original):

The trigonometric P\"oschl-Teller (PT) potential describes the diatomic molecular vibration. We have obtained the approximate solutions of the radial Schr\"odinger equation (SE) for the rotating trigonometric PT potential using the Nikiforov-Uvarov (NU) method. The energy eigenvalues and their corresponding eigenfunctions are calculated for arbitrary -states in closed form. In the low screening region, when the screening parameter the potential reduces to Kratzer potential. Further, some numerical results are presented for several diatomic molecules.

Journal Title, Volume, Page:

International Journal of Modern Physics E Vol. 22, No. 3
Year of Publication:

2013
Preferred Abstract (Original):

Approximate bound-state solutions of the Dirac equation with q-deformed Woods–Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term l(l+1)r^{-2}. Under some limitations, we can obtain solution for the RS Hulthén potential and the standard usual spherical WS potential (q = 1).

Journal Title, Volume, Page:

International Journal of Modern Physics E Vol. 21, No. 2 1250016 (13 pages)
Year of Publication:

2012
Preferred Abstract (Original):

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with Yukawa potential within the conventional approximation scheme to the centrifugal term for any -state. The semi-relativistic bound state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov-Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.

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:

Applied Mathematics and Computation, 216, 545–555
Year of Publication:

2010
Preferred Abstract (Original):

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 *κ* 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 (*l*=*l*˜=0, i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated.

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.