In the coefficients of Mie scattering Riccati- Bessel function appears. What is the significance of these functions in the context of Mie -scattering?
They are significantly solutions of the Strum-Liouville problem for the fields in spherical coordinates.
We can add that they describe the dependence of solution on a distance from the scattering center. They are obtained as solutions of the Sturm-Liouville problem for the radial part R(r) (\psi(r,\theta,\phi)=R(r) T(\theta) F(\phi)).
In the more general sense these functions show how significant are the eigenfunctions of the differential operators in the classical field theories of physics. It is also quite remarkable that the original paper by Gustav Mie, published in 1908, received over 4000 quotations (and this number is still growing).
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