Transfer matrix formulation of scattering theory in two and three dimensions

@article{Loran2016TransferMF,
  title={Transfer matrix formulation of scattering theory in two and three dimensions},
  author={Farhang Loran and Ali Mostafazadeh},
  journal={Physical Review A},
  year={2016},
  volume={93},
  pages={042707}
}
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous practical applications in different areas of physics. The problem of finding an analogous procedure in dimensions larger than one has been an important open problem for decades. We give a complete solution for this problem and discuss some of its applications. In… 
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