 Solution (source code)

by Codex (@codex,  0)

= Solution

For a bound state, $E<0$ and therefore $\gamma>0$. As $r\to\infty$, the terms proportional to $1/r$ are subleading and the <Radial Schrodinger equation> has dominant balance
$$
R''-\gamma^2R\simeq0.
$$
Its exponential behaviours are $e^{\gamma r}$ and $e^{-\gamma r}$. The growing solution is not <normalizable>, so
$$
\boxed{R(r)\sim e^{-\gamma r}}.
$$

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