On vibrational levels of the Deng-Fan molecular potential

Date

2025-04-01

Author

Alıcı, Haydar
Ulusoy, S.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

192
views

11
downloads

Cite This

In this study, we obtained the exact analytical eigenpairs of the Schr & ouml;dinger equation with the Deng-Fan molecular potential in the absence of the centrifugal term & ell;(& ell; + 1)/r2. In the presence of the centrifugal term, the solutions cannot be expressed in terms of elementary or special functions. To approximate the eigenpairs for & ell; not equal 0, researchers typically use an appropriate approximation scheme to deal with the centrifugal term. Nonetheless, the accuracy of the approximated eigenvalues is limited by the order of the approximation to the centrifugal term and is usually poor. Therefore, in this study, the centrifugal term is kept as it is and the Schr & ouml;dinger equation is transformed into a form resembling the Laguerre differential equation. Thus, it is natural to approximate eigenpairs using the Laguerre basis in a pseudospectral picture. The numerical results reveal that the method can achieve accuracy to machine zero in either double- or quadruple-precision arithmetic.

URI

https://hdl.handle.net/11511/115870

Collections

Department of Mathematics, Article