Abstract
The physics of atoms, molecules, and nuclei is correctly described by quantum mechanics (QM), but our physical intuition comes from classical mechanics (CM). Since the foundations of QM remain difficult to grasp, it is important to work out as far as possible the relations with CM. Until about 30 years ago, however, this task had been carried out successfully only for integrable systems, i.e., only where each degree of freedom could be treated separately in highly symmetrical systems. Even the spectra for simple systems such as the hydrogen-atom in a strong magnetic field (diamagnetic Kepler problem = DKP) or the donor-atom in a semiconductor (anisotropic Kepler problem = AKP) could not be understood, because 2 degrees of freedom are so strongly coupled that perturbation theory is of no help.
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