Generalized coherent states

Generalized coherent states are constructed for the Coulomb problem. Following a construction procedure proposed by Klauder [J. Phys. A 29, L293 (1996)], Rydberg atom coherent states are defined and analyzed. The relationship between decorrelation in time and delocalization in space is elucidated. Keplerian orbits are discussed. The connection with sharp Gaussian wave packets used to explain pump-probe experiments is made. This is achieved by introducing genuine Gaussian Klauder coherent states that are overcomplete, and permit a resolution of the identity operator. They decorrelate comparatively slowly, and remain spatially localized for many Keplerian periods.