Asymptotic behavior of atomic bound state wave functions

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 ${\mathrm{\Vert r}}_i^{\mu }\mathrm{\phi \Vert }$ , where r_i 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(r_i)φ‖, where h (x) is an exponentially increasing function. We finally indicate an exponentially decreasing pointwise bound for φ.