Quantum Chaos and Statistical Properties of Energy Levels: Numerical Study of the Hydrogen Atom in a Magnetic Field

Abstract

The transition to chaos in "the hydrogen atom in a magnetic field" is numerically studied and shown to lead to well-defined signature on the energy-level fluctuations. Upon an increase in the energy, the calculated statistics evolve from Poisson to Gaussian orthogonal ensemble according to the regular or chaotic character of the classical motion. Several methods are employed to test the generic nature of these distributions.