On generalized and approximative symmetry properties of quantum-mechanical and classical dynamical systems

We consider symmetry properties of differential equations in non-relativistic quantum mechanics and classical mechanics. Special emphasis is given to periodically driven systems. For a model system connections between symmetries of corresponding classical and quantal systems are established. The fundamental difference between variational symmetries and symmetries of the Euler-Lagrange-equations is discussed for the special case of classical mechanics. For nonintegrable systems with quasiregular regions in phase space we introduce the notion of approximate symmetry. As an example, we demonstrate the accuracy of such symmetry properties in certain domains of phase space for a periodically driven anharmonic oscillator. (orig.)