Abstarct: We well understand the Heisenberg principle which is the building block of quantum mechanics. The principle demonstrates the wave nature of particles and shows that the noncommutating quantities will not be simultaneously measurable. We also know that many hypotheses and principles of physics have been violated or modified as during time. In particular, the Heisenberg uncertainty principle needs to be modified at high energies. At high energies, the gravitational effects appear and indicate of the existence of so-called minimal length. The generalized uncertainty principle implies the reconsideration of quantum mechanics. Here, we have generalized quantum mechanics and has therefore become one of the most up-to-date research topics during past three decades. The present thesis has been written on the study of relativistic and nonrelativistic particles in generalized quantum mechanics. Here, we have generalized the uncertainty relations to three spatial dimensions, studied the time variation of oscillating system and calculated the thermodynamics properties of the N-particle harmonic system in the presence of minimal length. In addition we reviewed and studied the related relation in nuclear physics.