Rydberg states of atoms and molecules. Basic group theoretical and topological analysis

Rydberg states of atoms and molecules are studied within the qualitative ap proach-based primarily on topological and group theoretical analysis. The c orrespondence between classical and quantum mechanics is explored to apply the results of qualitative (topological) approach to classical mechanics de veloped by Poincare Lyapounov and Smale to quantum problems. The study of t he action of the symmetry group of the problems considered on the classical phase space enables us to predict qualitative features of the energy level patterns for quantum Rydberg operators. (C) 2001 Elsevier Science B.V. All lights reserved.