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.

We obtain analytical solutions of the two-body spinless Salpeter (SS) equation with the Yukawa potential within the conventional approximation scheme to the centrifugal term for any l-state. The semirelativistic bound-state energy spectra and the corresponding normalized wave functions are calculated by means of the Nikiforov–Uvarov (NU) method. We also obtain the numerical energy spectrum of the SS equation without any approximation to centrifugal term for the same potential and compare them with the approximated numerical ones obtained from the analytical expressions. It is found that the exact numerical results are in good agreement with the approximated ones for the lower energy states. Special cases are treated like the nonrelativistic limit and the solution for the Coulomb problem.

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