Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem

The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen atom. Here we discuss another close connection of classical trajectories and quantum mechanical states: the transient dynamics of objects around a nucleus. In this setup a comet (or an electron) is trapped for a while in the vicinity of an parent object (Jupiter or an atomic nucleus), but eventually escapes after many revolutions around the center of attraction.