Bound state solutions of D-dimensional Schr\"odinger equation with Eckart potential plus modified deformed Hylleraas potential

TL;DR

This paper solves the D-dimensional Schrödinger equation with Eckart and modified Hylleraas potentials using the Nikiforov-Uvarov method, deriving energy spectra and wave functions, including special cases like Hulthen and Rosen-Morse potentials.

Contribution

It introduces a generalized approach to solve the Schrödinger equation with complex potentials in multiple dimensions, providing explicit energy eigenvalues and wave functions.

Findings

Derived explicit energy eigenvalues and wave functions.

Analyzed special cases like Hulthen and Rosen-Morse potentials.

Numerical results for energy spectra and potentials.

Abstract

We study the D-dimensional Schr\"odinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discussed two special cases of this potential comprises of the Hulthen potential and the Rosen-Morse potential in 3-Dimensions. Numerical results are also computed for the energy spectrum and the potentials.