* Behavior for $r\to 0$ und $r\to \infty$ (10-20 min)

Verify that functions $\chi(r)$ with the following properties

$$\lim_{r \to 0} \chi(r)\propto r^{l+1},\quad \lim_{r \to \infty} \chi(r)\propto e^{-r\sqrt{-2mE/\hbar^2}},\quad E<0.$$ (46)

fulfill the radial part of the Schrödinger equation for `reasonable' potentials $U(r)$.