ASYMPTOTICS OF RYDBERG STATES FOR THE HYDROGEN-ATOM

The asymptotics of Rydberg states, i.e., highly excited bound states o f the hydrogen atom Hamiltonian, and various expectations involving th ese states are investigated. We show that suitable linear combinations of these states, appropriately rescaled and regarded as functions eit her in momentum space or configuration space, are highly concentrated on classical momentum space or configuration space Kepler orbits respe ctively, 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.