https://doi.org/10.1140/epjp/s13360-020-00337-4
Regular Article
Exact solution of Schrödinger equation in (anti-)de Sitter spaces for hydrogen atom
1
Laboratory of Photonic Physics and Nano-Materials (LPPNNM), Department of Matter Sciences, University of Biskra, Biskra, Algeria
2
Laboratory of Energy Engineering and Materials (LGEM), Department of Mechanics, University of Biskra, Biskra, Algeria
* e-mail: m.moumni@univ-biskra.dz
Received:
15
November
2019
Accepted:
17
March
2020
Published online:
30
March
2020
We write Schrödinger equation for the Coulomb potential in both de Sitter and anti-de Sitter spaces using the Extended Uncertainty Principle formulation. We use the Nikiforov–Uvarov method to solve the equations. The energy eigenvalues for both systems are given in their exact forms, and the corresponding radial wave functions are expressed in associated Jacobi polynomials for de Sitter space, while those of anti-de Sitter space are given in terms of Romanovski polynomials. We have also studied the effect of the spatial deformation parameter on the bound states in the two cases.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
