Thomas L., Villegas-Blas C.
Asymptotics of Rydberg States for the Hydrogen Atom
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ABSTRACT. The asymptotics of Rydberg states, i.e., highly excited bound states
of the hydrogen atom Hamiltonian, and various expectations involving
these states are investigated. We show that suitable linear
combinations of these states, appropriately rescaled and regarded as
functions either in momentum space or configuration space, are highly
concentrated on classical momentum space or configuration space Kepler
orbits respectively, for large quantum numbers. Expectations of
momentum space or configuration space functions with respect to these
states are related to time-averages of these functions over Kepler orbits.