Chaos is the generic term used to describe the irregular and unpredictable time evolution of physical systems. In classical mechanics, chaos may be defined in terms of the behavior of nearby particle trajectories. Since classical mechanics can be thought of as a special case of quantum mechanics, it is of interest to know how the irregularity of a classically chaotic system, influences the dynamics of the corresponding quantum system. One of the trade marks of quantum mechanics is the quantization of energy levels. It now seems apparent that chaos manifests itself in the distribution of the energy levels. A distribution of energy levels presupposes that the energy levels are discrete. However, if the electron is nearly stripped from its nucleus, the widths of the energy level spacings essentially go to zero and the energies become continuous. Continuous energies are also present in unbound quantum systems like the model studied in this project, the Hydrogen atom in an external magnetic field which is perpendicular to an electric field. This work will address how one looks for signatures of chaos in this model. We plan to check the validity of the meaning of the energy level distribution in an important energy range that has not been previously investigated.
