An exact solution of physical systems has a great importance. Especially, in the case of Schr”dinger equation there is only a few selected problems that can be exactly solvable. In this thesis work authors have developed an algebraic approach for the treatment of time-independent Schr”dinger equation with constant/non-constant masses within the frame of non-relativistic quantum theory. The model has been successfully applied in various fields of physics involving exactly/approximately solvable potentials such as non-central potentials, scattering theory and quantum systems with position-dependent masses in arbitrary dimensions. This model was then extended for the relativistic considerations in the light of Klein-Gordon and Dirac equations involving only bound quantum states.