{"paper":{"title":"Exact Solution of the Two-Dimensional Scattering Problem for a Class of $\\delta$-Function Potentials Supported on Subsets of a Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ali Mostafazadeh, Farhang Loran","submitted_at":"2017-08-20T19:01:22Z","abstract_excerpt":"We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\\zeta\\,\\delta(ax+by)g(bx-ay)$ where $\\zeta,a$, and $b$ are constants, $\\delta(x)$ is the Dirac $\\delta$ function, and $g$ is a real- or complex-valued function. We map this problem to that of $v(x,y)=\\zeta\\,\\delta(x)g(y)$ and give its exact and analytic solution for the following choices of $g(y)$: i) A linear combination of $\\delta$-functions, in which case $v(x,y)$ is a finite linear array of two-dimensional $\\delta$-functions; ii) A linear combina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06003","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}