Asymptotic behavior of atomic and molecular wave functions

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Abstract
The asymptotic form of bound-state wave functions is derived by analytic continuation of asymptotic scattering-state wave functions. The result is also regorously derived by using an approach that is independent of scattering theory. One aspect of the result is that the N electron wave function becomes the lowest accessible exact wave function for the remaining N - 1 electrons when one electron is far away from all the nuclei. This shows that the recently developed extended Koopmans' procedures are in principle exact for the first ionization energy.