Quantum mechanics originates from the study of the spectrum of hydrogen atom and the black body radiation and the development of this theory has been very successful for the study of atoms, the nucleus and the classification of elementary particles using SU (3) group. But the course of quantum mechanics in the second year should be revised to take account of these developments not only in terms of program but also from an educational point of view, especially for students of mathematical orientation. In this work we give an idea about the origin of quantum mechanics and we summarize the Schrodinger, the Dirac formalisms of quantum mechanic and the path integral. After exposing the Dirac's method of the oscillator we treat the Schwinger's approach of angular momentum. We present the theory of the central potential, the Quarks model and the classification: of chemical elements and elementary particles. We present a summary of the approaches of group theory. We present the theory of SU (3) and the decomposition of tensor product of SU (3). To take account of level of students we use in the applications our generating function method for its simplicity.
