Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

• Authors: Sameer Ikhdair , Ramazan Sever
• Languages of publication: EN

Abstracts

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.

Keywords

EN

energy eigenvalues and eigenfunctions; pseudoharmonic potential; ring-shaped potential; non-central potentials; Nikiforov and Uvarov method

Discipline

• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 04.20.Jb: Exact solutions

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 685-696

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Sameer Ikhdair

• Department of Physics, Near East University, Nicosia, TRNC, Mersin-10, Turkey

author

Ramazan Sever

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

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Identifiers

DOI

10.2478/s11534-008-0024-2