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.

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.

Approximate analytical solutions of spin and pseudospin symmetry limits of Dirac equation are reported for the generalized Pöschl-Teller scalar and vector potentials and a Coulomb tensor interaction by Nikiforov-Uvarov method. On the contrary to the cumbersome numerical procedures, the analytical approach followed here can be followed even by the undergraduate students.

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The Schrödinger equation under the ManningRosen potential is solved in arbitrary dimension via the quantum mechanical idea of supersymmetry. The Pekeris approximation is used to overcome the inconsistency of the potential with the centrifugal term. Comments on the energy eigenvalue behavior versus dimension are included. The inter-dimensional degeneracy for various orbital quantum number l and dimensions D are studied. The expectation values of some physical parameters are reported via the FeynmanHellmann theorem.