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In the radial function for a central potential, if we have a case such that $V(r)$ tends to $0$ much faster than $\frac{1}{r}$, how does $u(r)$ behave? And if $V(r)$ tends to $0$ like $\frac{1}{r}$, what changes in the previous argument? I know that, for $E<0$, it has to be in accordance with hydrogenic wave functions.

Artemisia
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