Comment on "Coherent states for the hydrogen atom"
Paolo Bellomo and C. R. Stroud, Jr.
Phys. Rev. A, 59, 900 (1999).
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Majumdar and Sharatchandra recently proposed a set of "coherent states"
for the hydrogen atom [Phys. Rev. A 56, R3322 (1997)]. These
states satisfy some of the typical properties of coherent states, such as,
for example, continuity in the parameters. The time evolution of these
states is given by the classical evolution of the angle variables, and the
expectation values of the quantum observables behave quasiclassically.
However, those authors also claimed that, although one does not obtain
exactly the same state after a Kepler period, the gross features of their
wave packets do not change. We show that this is not correct, and that
these wave packets do not remain localized on the classical variables, but
spread rapidly over the Keplerian orbit. The localization properties of
these states do not improve in the limit of large quantum numbers.
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