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    • 1.4: Scattering in 2D and 3D
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/01%3A_Scattering_Theory/1.04%3A_Scattering_in_2D_and_3D
      We now wish to consider scattering experiments in spatial dimension d≥2, which have a new and important feature. For d=1, the particle can only scatter forward or backward, but for d≥2 it can be s...We now wish to consider scattering experiments in spatial dimension d≥2, which have a new and important feature. For d=1, the particle can only scatter forward or backward, but for d≥2 it can be scattered to the side.
    • 6.1: A- Partial Wave Analysis
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/06%3A_Appendices/6.01%3A_A-_Partial_Wave_Analysis
      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 \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_{\ell' m'} \Big(S_{\ell m, \ell' m'} - \delta_{\ell \ell'}\delta_{mm'}\Big) e^{i\ell'\pi/2} \, Y_{\ell' m'}^*(\hat{\mathbf{k}}_i)\; \Psi_i.\end{align} 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}…

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