{"paper":{"title":"Schr\\\"odinger operators with concentric $\\delta$--shell interactions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Masahiro Kaminaga","submitted_at":"2026-02-10T03:41:00Z","abstract_excerpt":"We study Schr\\\"odinger operators on $\\mathbb R^3$ with finitely many concentric spherical $\\delta$-shell interactions. The operators are defined by the quadratic form method and are described by continuity across each shell together with the usual jump condition for the radial derivative. Using a boundary integral approach based on the free Green kernel and single-layer potentials, we derive an explicit resolvent representation for an arbitrary number of shells with bounded coupling strengths. This yields a concrete Kre\\u{\\i}n-type formula and a boundary operator whose noninvertibility charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09376","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.09376/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}