Scattering in the Poincaré disk and in the Poincaré upper half-plane

Jesus, Anderson L. de; Maioli, Alan C.; Schmidt, Alexandre G. M.

doi:10.1088/1402-4896/ac3d4c

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2022

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Cited by 2 publications

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“…Using this approach, which we developed for two [43,44] and three-dimensional [45,46] scattering problems, we can exactly solve the LS equation. The same methodology can be used to tackle scattering problems in non-Euclidean geometries [47].…”

Section: Introductionmentioning

confidence: 99%

Non-relativistic scattering by a shield barrier and by an elliptical aperture

Schmidt¹,

Jesus²

2022

Phys. Scr.

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We study the non-relativistic quantum mechanical scattering of a plane wave by a shield barrier and an elliptical aperture modeled as Dirac delta functions running along a coordinate surface of the sphero-conal coordinate system. The scattering problem is formulated via Lippmann-Schwinger (LS) equation in the position representation. In order to solve the LS equation, we first calculate the free Green's function of the problem and obtain its bilinear expansion in terms of the eigenfunctions of the scalar Helmholtz equation—which are products of spherical Bessel (or first kind Hankel) functions and Lamé polynomials. Such bilinear expansion allows us to obtain an integral equation with a separable kernel and solve the scattering problem. Then, we calculate the wavefunctions in the internal and external domains and the scattering amplitudes.

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