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‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States

Abstract : Summary We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. These integrals arise in wave and quantum mechanical scattering problems of open systems containing cylindrical or spherical scatterers, particularly when those problems are considered in the framework of complex resonant modes. Explicit representations are obtained for the integrals, building on those in the 1992 paper by McPhedran, Dawes and Scott. Attention is paid to those sums with a distributive part arising as the Gaussian tends towards the unit function. In this limit, orthogonality and normalisability of complex modes are investigated.
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https://hal-amu.archives-ouvertes.fr/hal-03222799
Contributor : Patrick Ferrand <>
Submitted on : Monday, May 10, 2021 - 2:56:12 PM
Last modification on : Monday, May 17, 2021 - 12:55:47 PM

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R Mcphedran, B Stout. ‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States. Quarterly Journal of Mechanics and Applied Mathematics, Oxford University Press (OUP), 2020, 73 (2), pp.119-139. ⟨10.1093/qjmam/hbaa004⟩. ⟨hal-03222799⟩

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