English

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

Mathematical Physics 2023-10-03 v1 math.MP Quantum Physics

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.

Keywords

Cite

@article{arxiv.2203.13866,
  title  = {Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments},
  author = {Farhang Loran and Ali Mostafazadeh},
  journal= {arXiv preprint arXiv:2203.13866},
  year   = {2023}
}

Comments

10 pages, contributed to the proceedings of RDP online PhD school and workshop "Aspects of Symmetry" (Regio2021), 8-12 November 2021