Journal Title, Volume, Page:

Journal of Molecular Structure: THEOCHEM Volume 855, Issues 1–3, Pages 13–17
Year of Publication:

2008
Preferred Abstract (Original):

The polynomial solution of the *D*-dimensional Schrödinger equation for a special case of Mie potential is obtained with an arbitrary *l*≠0 states. The exact bound state energies and their corresponding wave functions are calculated. The bound state (real) and positive (imaginary) cases are also investigated. In addition, we have simply obtained the results from the solution of the Coulomb potential by an appropriate transformation.

Journal Title, Volume, Page:

Journal of Molecular Structure: THEOCHEM 806, 155–158
Year of Publication:

2007
Preferred Abstract (Original):

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum
Journal Title, Volume, Page:

Molecular Physics: An International Journal at the Interface Between Chemistry and Physics Volume 110, Issue 13, 1415-1428
Year of Publication:

2012
Preferred Abstract (Original):

We solve the parametric generalized effective Schrödinger equation with a specific choice of position-dependent mass function and Morse oscillator potential by means of the Nikiforov–Uvarov method combined with the Pekeris approximation scheme. All bound-state energies are found explicitly and all corresponding radial wave functions are built analytically. We choose the Weyl or Li and Kuhn ordering for the ambiguity parameters in our numerical work to calculate the energy spectrum for a few (H
Journal Title, Volume, Page:

International Journal of Modern Physics C Vol. 19, No. 9, 1425-1442
Year of Publication:

2008
Preferred Abstract (Original):

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

Journal Title, Volume, Page:

Central European Journal of Physics September, Volume 6, Issue 3, pp 697-703
Year of Publication:

2008
Preferred Abstract (Original):

Making an ansatz to the wave function, the exact solutions of the *D*-dimensional
radial Schrödinger equation with some molecular potentials, such as
pseudoharmonic and modified Kratzer, are obtained. Restrictions on the
parameters of the given potential, *δ* and *ν* are also given, where *η* depends on a linear combination of the angular momentum quantum number *ℓ* and the spatial dimensions *D* and *δ* is a parameter in the ansatz to the wave function. On inserting *D* = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

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:

Int. J. Mod. Phys. C 18, 1571
Year of Publication:

2007
Preferred Abstract (Original):

Utilizing an appropriate ansatz to the wave function, we
reproduce the exact bound-state solutions of the radial Schrödinger
equation to various exactly solvable sextic anharmonic oscillator and
confining perturbed Coulomb models in D-dimensions. We show that the
perturbed Coulomb problem with eigenvalue E can be transformed to a
sextic anharmonic oscillator problem with eigenvalue .
We also check the explicit relevance of these two related problems in
higher-space dimensions. It is shown that exact solutions of these
potentials exist when their coupling parameters with k = D +2ℓ appearing
in the wave equation satisfy certain constraints.

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:

IL Nuovo Cimento, 115B, No. 12, 1397
Year of Publication:

2000
Preferred Abstract (Original):

We consider an exactly solvable model, namely the interaction that is one of the point interactions. For the repulsive case, we drive the reflection and transmission coefficients. It is shown that the coefficients satisfy the unitarity of the scattering matrix. If the incident particle has a certain energy, then the barrier becomes perfectly reflective. Furthermore, it is shown that the barrier becomes completely transmittive for the high-energy behavior. For the attractive case, we examine both the bound states and the scattering states. It is shown that there exist two bound states and for the scattering case it is demonstrated that one recovers the same reflection and transmission coefficients that were obtained for the repulsive case.