Elliptic Atomic States

  • Antoine Bommier
  • Dominique Delande
  • Jean-Claude Gay
Part of the NATO ASI Series book series (NSSB, volume 212)


We solve here part of the Lorentz-Schrödinger conjecture bearing on the definition of atomic states which mimic the classical Bohr-Sommerfeld-Kepler orbits with minimum quantum fluctuations. These states are uniquely defined from symmetry considerations and are stationary states of the Coulomb hamiltonian. They exhibit the best spatial localization it is possible to achieve within quantum-mechanical constraints, on a classical Kepler ellipse. Explicit expansions of these “elliptic” states onto the spherical and parabolic basis are given. We further show that the experimental production of such states is possible from a crossed electric and magnetic fields arrangement combined with laser excitation. The method has already been experimentally demonstrated in the special case of the production of circular Rydberg atoms. We finally conclude with some applications of this technique to spectroscopy and fundamental questions.


Angular Momentum Coherent State Rydberg Atom Circular State Heisenberg Uncertainty Relation 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Antoine Bommier
    • 1
  • Dominique Delande
    • 1
  • Jean-Claude Gay
    • 1
  1. 1.Laboratoire de Spectroscopie Hertzienne de l’Ecole Normale SupérieureParis Cedex 05France

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