{"paper":{"title":"A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.optics"],"primary_cat":"quant-ph","authors_text":"Ali Mostafazadeh, Farhang Loran","submitted_at":"2017-11-03T12:50:26Z","abstract_excerpt":"We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)=\\chi_a(x)[v_0(x)+ v_1(x)e^{i\\alpha y}]$, where $\\chi_a(x):=1$ for $x\\in[0,a]$, $\\chi_a(x):=0$ for $x\\notin[0,a]$, $v_j(x)$ are real or complex-valued functions, $\\chi_a(x)v_0(x)$ is an exactly solvable scattering potential in one dimension, and $\\alpha$ is a positive real parameter.If $\\alpha$ exceeds the wavenumber $k$ of the incident wave, the scattered wave does not depend on the choice of $v_1(x)$. In particular, $v(x,y)$ is invisible if $v_0(x)=0$ and $k<\\alpha$. For $k>\\alpha$ and $v_1(x)\\neq 0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01132","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"}