Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential
| Autor: | Sameer M. Ikhdair, Ramazan Sever |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
non-central potentials
Physics Ring (mathematics) 04.20.jb pseudoharmonic potential energy eigenvalues and eigenfunctions QC1-999 General Physics and Astronomy Eigenfunction 03.65.-w Schrödinger equation symbols.namesake 03.65.fd 0365.ge Laguerre polynomials symbols Jacobi polynomials ring-shaped potential Beta (velocity) nikiforov and uvarov method Energy (signal processing) Eigenvalues and eigenvectors Mathematical physics |
| Zdroj: | Open Physics, Vol 6, Iss 3, Pp 685-696 (2008) |
| ISSN: | 2391-5471 |
| DOI: | 10.2478/s11534-008-0024-2 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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