Unitarity and reflection identities for a partial-wave S-matrix
= Unitarity and reflection identities for a partial-wave S-matrix
For a real central potential and real $k$, radial-current conservation gives $S_l(k)^*S_l(k)=1$. Invariance of the radial equation under $k\mapsto-k$ gives $S_l(k)S_l(-k)=1$, so a continuous phase convention has $\delta_l(-k)=-\delta_l(k)$.