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

For the hydrogen atom in crossed, perpendicular, static electric and magnetic fields we show the existence of three elementary Kepler ellipses, two in the plane perpendicular to the magnetic field and one, three-dimensional, largely perpendicular to the electric field. They are determined from the symmetry properties in the low field limit, occurring for all external field combinations. Their parameter dependences and stability properties are analysed in detail. In the case that the orbits are stable the corresponding maximum orientated quantum states are 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.