Quadrupole coupling against finite differences

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Reference
quadrupole coupling against finite differences
Kind
method: an independent formulation inside this repo (a scattering matrix, a plane-wave superposition, a quadrature): proves the formulation
Calculated
rates, pattern
Agreement
—
A quadrupole 47 nm from the centre (k = 0.013 nm⁻¹): its coupling to each multipole order against finite differences (1/6) Σ Q_ij ∂_j W_i of the vector spherical waves W = M + N (Bohren & Huffman's, the axial m = 0 family shown; the difference covers all five families and M − N), PyStratify's closed-form functional against central differences of the 40-digit waves. The regular wave fades with order at this distance and the outgoing one grows.
1234567810⁻¹¹10⁻⁸10⁻⁵10⁻²1010⁴10⁷10¹⁰order ℓ|coupling|
regular wave (ψ), PyStratify outgoing wave (ξ), PyStratify regular wave (ψ), finite differences outgoing wave (ξ), finite differences
Hover to read values.
  • largest relative difference over every family: 1.17×10⁻¹⁴
  • PyStratify the lines, the reference the circles

Run it yourself: sphere_emitter_checks.py · test_quadrupoles.py · figures.py · SPHERE_EMITTER_CHECKS.md on GitHub, PyStratify 97e52a9