Abstarct: In this thesis intend to introduce a quasi-exactly solvable method by using group theory . then, using this method we study non-relativistic and relativistic system (fermionic and bosonic systems). In recent years, much attention has been paid to the study of the relativistic and non-relativistic wave equations in between, the solution of the Dirac equation as a relativistic wave equation, that leads to acceptable physical results is very important, and plays an important role in relativistic quantum mechanics. Physicists tried to solve the Dirac equation with physical potentials, and the number of exact solutions in this area is increasing. Then, in them different standard methods have been used. One of these standard method is to solve the Dirac equation in algebraic method using group theory. In this thesis, the Dirac equation is presented as a relativistic wave equation in the presence of vector and scalar potential and differential equations for each spinor are solved analytically, and the function of the wave of fermions and their energy spectrum. In the following, the Dirac equation for coulomb potential is investigated in space-time coordinates by a quasi-exactly solvable method. Finally, the wave function and the energy spectrum of the fermions are calculated at the coulomb potential. Also, for bosonic systems, in the presence of vector potential and scalar, the wave function of the boson energy is investigated by a quasi-exactly solvable method. Today, number of potentials in non-relativistic quantum mechanics are exact solved and their energy spectrum and wave functions are obtained. In this thesis, we examine the potential of non-relativistic systems for the Killingbeck potential using a quasi-exactly solvable method. We also evaluate the distribution of energy-momentum using the well-known complexes of Landau-Lifshitz and Einstein and Papapetru in the two metrics of som-Raychaudhuri and godel metric. In the last section, we study and analyze the tavis-cummings method and its relation to the quasi-exactly solvable Hamiltonian of the SL(2) group and then use the Heun-biconfluent equation to solve it in different forms withdifferent potentials.