{"paper":{"title":"Approximation and equidistribution of phase shifts: spherical symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Jesse Gell-Redman, Kiril Datchev, Peter Humphries","submitted_at":"2012-11-21T08:37:46Z","abstract_excerpt":"Consider a semiclassical Hamiltonian \\begin{equation*}\n  H_{V, h} := h^{2} \\Delta + V - E \\end{equation*} where $h > 0$ is a semiclassical parameter, $\\Delta$ is the positive Laplacian on $\\mathbb{R}^{d}$, $V$ is a smooth, compactly supported central potential function and $E > 0$ is an energy level. In this setting the scattering matrix $S_h(E)$ is a unitary operator on $L^2(\\mathbb{S}^{d-1})$, hence with spectrum lying on the unit circle; moreover, the spectrum is discrete except at $1$.\n  We show under certain additional assumptions on the potential that the eigenvalues of $S_h(E)$ can be d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4959","kind":"arxiv","version":2},"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"}