{"paper":{"title":"Boundary perturbations and the Helmholtz equation in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"G. Hazra, S. Panda","submitted_at":"2012-12-07T09:52:40Z","abstract_excerpt":"We propose an analytic perturbative scheme for determining the eigenvalues of the Helmholtz equation, $(\\nabla^2 + k^2) \\psi = 0$, in three dimensions with an arbitrary boundary where $\\psi$ satisfies either the Dirichlet boundary condition ($\\psi =0$ on the boundary) or the Neumann boundary condition (the normal gradient of $\\psi$, $\\frac{\\partial \\psi}{\\partial n}$ is vanishing on the boundary). Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to best of our knowledge the formulation in three dimensions is proposed for the first time. In thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1565","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"}