Classical Limit of a Hydrogen Atom

by

Zagorka D. Gaeta
(1995)

This thesis explores the classical limit of the hydrogen atom by focusing on the questions of existence, properties, excitation, and detection of a classical-limit state of hydrogen. A classical-limit state is a spatially well localized wave packet whose motion is described by the Kepler laws.

It has long been known that a hydrogenic state with such properties cannot exist for infinite time. However, the circular-orbit wavepacket and the elliptic-orbit wave packet look and behave like classical-limit states over a limited period of time.

Such wave packets have both classical and quantum character, each of which intermittently dominates the evolution. A detailed study of the short and long-term dynamics of the circular-orbit wave packet reveals a rich dynamical structure which is characterized with continuous spreading and reforming of the wave packet.

While there have been a number of successful experiments in which Rydberg wave packets in alkali atoms were excited, no attempts to excite a wave packet localized in all three dimensions that travels in a classical Kepler orbit have been reported. We describe physical phenomena that serve as basis of experimental techniques for the excitation and detection of such wave packets.

The physical phenomena in question arise in the interaction between a hydrogen atom and an electric field pulse. Depending on the strength of the electric field and duration of the pulse, this interaction can be utilized to produce a desired superposition of states within a single energy manifold, or a superposition of particular states from several neighboring manifolds. We propose techniques for the excitation of circular- and elliptic-orbit wave packets, which utilize electric pulses whose duration is much shorter than a Kepler period. We also propose techniques for the preparation of an elliptic state of arbitrary eccentricity, which utilize electric pulses whose fields are too weak to mix states from different energy manifolds. The properties of the wave packets that can be excited using the proposed techniques are studied.

Circular- and elliptic-orbit wave packets can be detected using an ionizing short electric pulse. We propose pump-probe experiments that combine the excitation and detection and describe ionization signals that can be expected.

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Last modified 13 September 2006