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  1. 3 Open Physics

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  1. 2 2008

  2. 1 2007

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  1. 3 Ikhdair S.

  2. 3 Sever R.

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Exact solutions of the radial Schrödinger equation for some physical potentials

100%
Ikhdair S., Sever R.
Open Physics
|
2007
|
vol. 5
|
issue 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.
2
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Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

100%
Ikhdair S., Sever R.
Open Physics
|
2008
|
vol. 6
|
issue 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.
3
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On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

86%
Ikhdair S., Sever R.
Open Physics
|
2008
|
vol. 6
|
issue 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.
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