Asymptotic behavior of atomic bound state wave functions

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In the present paper we investigate the asymptotic properties of an exact bound state wave function φ of an n-electron atomic system within the infinite nuclear mass approximation and neglecting relativistic effects. An explicit upper bound is derived for ‖riμφ‖, where ri denotes the distance of the ith electron from the nucleus and μ = 1,2,3,⋯. We are then able to derive upper bounds for expressions like ‖h(ri)φ‖, where h (x) is an exponentially increasing function. We finally indicate an exponentially decreasing pointwise bound for φ.