= Solution
For real $k$, conservation of the radial <probability current>, equivalently constancy of the radial Wronskian, equates the incoming and outgoing fluxes and gives
$$
S_l(k)^*S_l(k)=1.
$$
For a real potential, the regular radial solution depends on $k$ through $k^2$. Comparing its asymptotic form at $k$ and $-k$ therefore gives
$$
S_l(k)S_l(-k)=1.
$$
The first identity places $S_l(k)$ on the unit circle, so
$$
S_l(k)=e^{2i\delta_l(k)}
$$
for a real phase shift. Choosing the phase continuously, the second identity gives
$$
\boxed{\delta_l(-k)=-\delta_l(k).}
$$
These are the <unitarity and reflection identities for a partial-wave S-matrix>.
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