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1
Content available remote On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz
100%
Ikhdair S. , Sever R.
Open Physics
|
2008
|
tom 6
|
nr 3
697-703
EN
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.
2
Content available remote Exact solutions of the radial Schrödinger equation for some physical potentials
100%
Ikhdair S. , Sever R.
Open Physics
|
2007
|
tom 5
|
nr 4
516-527
EN
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.
3
Content available remote Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry
100%
Ikhdair S. , Sever R.
Open Physics
|
2010
|
tom 8
|
nr 4
652-666
EN
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 = $$ \tilde l $$ = 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.
4
Content available remote Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential
100%
Ikhdair S. , Sever R.
Open Physics
|
2008
|
tom 6
|
nr 3
685-696
EN
A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.
5
Content available remote Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential
100%
Ikhdair S. , Sever R.
Open Physics
|
2008
|
tom 6
|
nr 1
141-152
EN
The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.
6
Content available remote Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any κ-value
80%
Arda A. , Sever R. , Tezcan C.
Open Physics
|
2010
|
tom 8
|
nr 5
843-849
EN
The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-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.
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