We study the D-dimensional Schrödinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov (NU) method, we calculate the corresponding eigenfunctions and eigenvalues.

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Based on the significant role of spin and pseudospin symmetries in hadron and nuclear spectroscopy, we have investigated Dirac equation under scalar and vector potentials of cotangent hyperbolic form besides a Coulomb tensor interaction via an approximate analytical scheme. The considered potential for small potential parameter resembles the well-established Kratzer potential. In addition, we see how the tensor term removes the degeneracy of doublets. After an acceptable approximation, namely a Pekeris-type one, we see that the problem is simply solved via the quantum mechanical idea of supersymmetry without having to deal with the cumbersome, complicated and time-consuming numerical programming.

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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.

Approximate analytical solutions of the D-dimensional Klein-Gordon equation are obtained for the scalar and vector general Hulthén-type potential and position-dependent mass with any l by using the concept of supersymmetric quantum mechanics (SUSYQM). The problem is numerically discussed for some cases of parameters.