E. Flothmann et al., THE KEPLER ELLIPSES OF THE HYDROGEN-ATOM IN CROSSED ELECTRIC AND MAGNETIC-FIELDS, Journal of physics. B, Atomic molecular and optical physics, 27(13), 1994, pp. 2821-2833
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.