# Radial function in quantum mechanics

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.

• Could you define things a little bit more clearly, I assume by $u\left( r \right)$ you mean the radial part of the wavefunction? – Chris2807 Jan 21 '15 at 16:44
• Yes that's correct. Sorry I'm on my phone haha so a bit lazy to type :/ – Artemisia Jan 21 '15 at 16:56
• think you might find what you are looking for here physics.stackexchange.com/questions/12892/… and links within – Chris2807 Jan 21 '15 at 16:58