THE KEPLER ELLIPSES OF THE HYDROGEN-ATOM IN CROSSED ELECTRIC AND MAGNETIC-FIELDS

For the hydrogen atom in crossed, perpendicular, static electric and m agnetic fields we show the existence of three elementary Kepler ellips es, two in the plane perpendicular to the magnetic field and one, thre e-dimensional, largely perpendicular to the electric field. They are d etermined from the symmetry properties in the low field limit, occurri ng for all external field combinations. Their parameter dependences an d stability properties are analysed in detail. In the case that the or bits are stable the corresponding maximum orientated quantum states ar e identified. For states with sufficient low principal quantum numbers the total splitting of a given n-shell is described by semiclassical quantization of these three Kepler ellipses.