Schrödinger equation | An-Najah Staff

On Solutions of the Schrödinger Equation for Some Molecular Potentials: Wave Function Ansatz

Sun, 2013-09-15 13:26 — Sameer. Ikhdair

Journal Title, Volume, Page:

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

Year of Publication:

2008

Link:

http://link.springer.com/content/pdf/10.2478/s11534-008-0060-y.pdf

Authors:

Sameer M. Ikhdair

Department of Physics, Near East University, Nicosia, North Cyprus, Mersin-10, Turkey

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

Ramazan Sever

Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

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.

Influence of External Fields on the Killingbeck Potential: Quasi Exact Solution

Sun, 2013-09-15 09:20 — Sameer. Ikhdair

Journal Title, Volume, Page:

Modern Physics Letters B , Volume 27, Issue 24

Year of Publication:

2013

Link:

http://www.worldscientific.com/doi/abs/10.1142/S0217984913501765?journalCode=mpl...

Authors:

S. M. IKHDAIR

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

M. HAMZAVI

Department of Science and Engineering, Abhar Branch, Islamic Azad University, Abhar, Iran

Preferred Abstract (Original):

The Killingbeck potential consists of oscillator potential plus Cornell potential, i.e. ar²+ br - c/r, that it has received a great deal of attention in particle physics. In this paper, we study the energy levels and wave function for arbitrary m-state in two-dimensional (2D) Schrödinger equation (SE) with a Killingbeck potential under the influence of strong external uniform magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the Schrödinger equation with Killingbeck potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.

Approximate Analytic Eigensolutions of the Hellmann Potential with any Arbitrary Angular Momentum

Sun, 2013-09-15 07:59 — Sameer. Ikhdair

Journal Title, Volume, Page:

Z. Naturforsch. XXX, 1 – 8

Year of Publication:

2013

Authors:

Sameer M. Ikhdair

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

Current Affiliation:

Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine

[email protected]

Babatunde J. Falaye

Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria

Preferred Abstract (Original):

The parametric Nikiforov–Uvarov (pNU) and asymptotic iteration method (AIM) are applied to study the approximate analytic bound state eigensolutions (energy levels and wave functions) of the radial Schrödinger equation (SE) for the Hellmann potential which represents the superposition of the attractive Coulomb potential (a=r) and the Yukawa potential bexp(- $\delta \!\,$ r) /r of arbitrary strength b and screening parameter $\delta \!\,$ in closed form. The analytical expressions to the energy eigenvalues E yield quite accurate results for a wide range of n,l in the limit of very weak screening but the results become gradually worse as the strength b and the screening coefﬁcient $\delta \!\,$ increase. The calculated bound state energies have been compared with available numerical data. Special cases of our solution like pure Coulomb and Yukawa potentials are also investigated.

An Alternative Simple Solution of the Sextic Anharmonic Oscillator and Perturbed Coulomb Problems

Thu, 2013-09-12 11:01 — Sameer. Ikhdair

Journal Title, Volume, Page:

Int. J. Mod. Phys. C 18, 1571

Year of Publication:

2007

Link:

http://www.worldscientific.com/doi/abs/10.1142/S0129183107011583

Authors:

Sameer M Ikhdair

Department of Physics, Near East University Nicosia, North Cyprus, Mersin-10, Turkey

Current Affiliation:

Department of Physics, An-Najah National University, Nablus, Palestine

[email protected]

Ramazan Sever

Department of Physics, Middle East Technical University 06531 Ankara, Turkey

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.