In this thesis, I study the group theoretic structure of the Schrodinger equations of simple systems by making use of a new systematic method. Group theoretic analysis of Schrodinger equations have been made previously by numerous physicists. The groups found may be classified as: a) geometrical groups; b) dynamical degeneracy groups; c) dynamical groups The geometrical group arises simply from the spatial symmetry of the system. Although the geometrical groups are very useful, they are not very interesting from the physical viewpoint. On the other hand, the study of the dynamical degeneracy groups and the dynamical group is very attractive because it reflects the dynamic of the system. Extensive studies have previously been made by other authors on systems which exhibit nontrivial degeneracy (accidental degeneracy). It turns out that all the states which belong to the same energy level provide a basis for a unitary irreducible representation of some compact group, and the group itself is generated by a set of constants of the motion. These groups are called “dynamical degeneracy groups”. Detailed discussion on degeneracy groups will be found in the paper by McIntosh alluded to above.