Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments

• URL: http://arxiv.org/abs/2203.13866v1
• Date: Fri, 25 Mar 2022 19:07:13 GMT
• Title: Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments
• Authors: Farhang Loran and Ali Mostafazadeh
• Abstract summary: We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions. We discuss its utility in circumventing the ultraviolet divergences one encounters in solving the Lippman-Schwinger equation for delta-function potentials in two and three dimensions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in circumventing the ultraviolet divergences one encounters in solving the Lippman-Schwinger equation for delta-function potentials in two and three dimensions. We also use it to construct complex scattering potentials displaying perfect omnidirectional invisibility for frequencies below a freely preassigned cutoff.

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