We solve the D-dimensional Schr€ odinger equation under the Hua potential by using a Pekeris-type approximation and the supersymmetry quantum mechanics. The reliability of the spectrum is checked via a comparison with the finite difference method. This interaction resembles Eckart, Morse, and Manning-Rosen potentials. Some useful quantities are reported via the Hellmann-Feynman Theorem.

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In this paper, we present solutions of the Klein-Gordon equation for the improved Manning—Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.