The scattering matrix relation can then be re-written as \[\begin{align} c^+_\mu &= c^+_{i,\mu} + c^+_{s,\mu} = \sum_{\mu\nu} S_{\mu\nu} c^-_{i,\nu} \\ \Rightarrow \;\;\; c^+_{s,\ell m} &= 2 \pi \sum_...The scattering matrix relation can then be re-written as c+μ=c+i,μ+c+s,μ=∑μνSμνc−i,ν⇒c+s,ℓm=2π∑ℓ′m′(Sℓm,ℓ′m′−δℓℓ′δmm′)eiℓ′π/2Y∗ℓ′m′(ˆki)Ψi. Using this, the scattered wavefunction can be written as \[\begin{align}\begin{aligned}\psi_s(\mathbf{r}) &= \sum_{\ell m} c^+_{s,\ell m} h_{\ell}…
