pseudoharmonic potential

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Exact Polynomial Eigensolutions of the Schrödinger Equation for the Pseudoharmonic Potential

Journal Title, Volume, Page: 
Journal of Molecular Structure: THEOCHEM 806, 155–158
Year of Publication: 
2007
Authors: 
Sameer 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
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
Preferred Abstract (Original): 
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By a proper transformation, this problem is also solved very simply by using the known eigensolutions of anharmonic oscillator potential.
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A Quantum Pseudodot System with Two-Dimensional Pseudoharmonic Oscillator In External Magnetic and Aharonov-Bohm Fields

Journal Title, Volume, Page: 
Physica B: Condensed Matter Volume 407, Issue 21, 4198–4207
Year of Publication: 
2012
Authors: 
Sameer M. Ikhdair
Physics Department, Near East University, 922022 Nicosia, North Cyprus, Turkey
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Majid Hamzavi
Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran
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.

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Exact Bound States of the D-Dimensional Klein Gordon Equation with Equal Scalar and Vector Ring-Shaped Pseudoharmonic Potential

Journal Title, Volume, Page: 
International Journal of Modern Physics C Vol. 19, No. 9, 1425-1442
Year of Publication: 
2008
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
Ramazan Sever
Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
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.


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

Journal Title, Volume, Page: 
Central European Journal of Physics September, Volume 6, Issue 3, pp 697-703
Year of Publication: 
2008
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
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 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.

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Exact Solutions of the D-dimensional Schrödinger Equation for a Ring–shaped Pseudoharmonic Potential

Journal Title, Volume, Page: 
Central European Journal of Physics September, Volume 6, Issue 3, pp 685-696
Year of Publication: 
2008
Authors: 
Sameer M. Ikhdair
Department of Physics, Near East University, Nicosia, TRNC, Mersin-10, Turkey
Current Affiliation: 
Department of Physics, Faculty of Science, An-Najah National University, Nablus, Palestine
Ramazan Sever
Department of Physics, Middle East Technical University, 06531, Ankara, Turkey
Preferred Abstract (Original): 

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . 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.

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Exact Solutions of the Radial Schrödinger Equation for Some Physical Potentials

Journal Title, Volume, Page: 
Central European Journal of Physics December, Volume 5, Issue 4, pp 516-527
Year of Publication: 
2007
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
Ramazan Sever
Department of Physics, Middle East Technical University, 06531, Ankara, Turkey
Preferred Abstract (Original): 

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.

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