Coherent states for the hydrogen atom

Details Coherent states for the hydrogen atom Coherent states for the hydrogen atom

1997-08-05

arxiv.org/abs/quant-ph/9708010v2

Phys. Rev. A56 (1997) R3322

Physics

Quantum Physics

9 pages, 2 figures, minor change in language and journal reference added

Scientific paper

10.1103/PhysRevA.56.R3322

We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable corresponding to the position on the orbit is now non-compact and we do not get exactly the same state after one period. However the gross features do not change. In particular the wave packet remains peaked around the labels.) ii) Resolution of identity using this overcomplete set involves exactly the classical phase space measure. iii) Semi-classical limit is related to Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave packets in position and momentum.

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