{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4VNQU4BX4YS2QEIWJUT6YMMVCL","short_pith_number":"pith:4VNQU4BX","schema_version":"1.0","canonical_sha256":"e55b0a7037e625a811164d27ec319512c9c9e42f692a561cfca70d00294a8f7d","source":{"kind":"arxiv","id":"1611.04107","version":1},"attestation_state":"computed","paper":{"title":"Passage through a potential barrier and multiple wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"D. R. Yafaev","submitted_at":"2016-11-13T10:06:36Z","abstract_excerpt":"Consider the semiclassical limit, as the Planck constant $\\hbar\\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\\\"odinger operator, the Bohr-Sommerfeld quantization condition is satisfied at least for one potential well. The proof of this result relies on a study of real wave functions in a neighborhood of a potential barrier. We show that, at least from one side, the barrier fixes the phase of wave functions in the same way as a potential barrier of infinite width. On the other hand, i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.04107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-13T10:06:36Z","cross_cats_sorted":["math-ph","math.CA","math.FA","math.MP"],"title_canon_sha256":"36ee55473787f55a6589fcb6cfeecb650ac115998092453394332650e9e441d1","abstract_canon_sha256":"54e5804475d5a211701ee0a1ab1fded581f4fa8ae03401e36948d833195ca924"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:17.527225Z","signature_b64":"FlZQnDf3vyTsopookW9KPbOkJaISX4S7Qp5E4QjKsSdsGhN/LA+pKpmvhIOMAon1dYo9W+c77592b5HhlUM0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e55b0a7037e625a811164d27ec319512c9c9e42f692a561cfca70d00294a8f7d","last_reissued_at":"2026-05-18T00:59:17.526597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:17.526597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Passage through a potential barrier and multiple wells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"D. R. Yafaev","submitted_at":"2016-11-13T10:06:36Z","abstract_excerpt":"Consider the semiclassical limit, as the Planck constant $\\hbar\\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\\\"odinger operator, the Bohr-Sommerfeld quantization condition is satisfied at least for one potential well. The proof of this result relies on a study of real wave functions in a neighborhood of a potential barrier. We show that, at least from one side, the barrier fixes the phase of wave functions in the same way as a potential barrier of infinite width. On the other hand, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04107","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.04107","created_at":"2026-05-18T00:59:17.526687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04107v1","created_at":"2026-05-18T00:59:17.526687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04107","created_at":"2026-05-18T00:59:17.526687+00:00"},{"alias_kind":"pith_short_12","alias_value":"4VNQU4BX4YS2","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4VNQU4BX4YS2QEIW","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4VNQU4BX","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL","json":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL.json","graph_json":"https://pith.science/api/pith-number/4VNQU4BX4YS2QEIWJUT6YMMVCL/graph.json","events_json":"https://pith.science/api/pith-number/4VNQU4BX4YS2QEIWJUT6YMMVCL/events.json","paper":"https://pith.science/paper/4VNQU4BX"},"agent_actions":{"view_html":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL","download_json":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL.json","view_paper":"https://pith.science/paper/4VNQU4BX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04107&json=true","fetch_graph":"https://pith.science/api/pith-number/4VNQU4BX4YS2QEIWJUT6YMMVCL/graph.json","fetch_events":"https://pith.science/api/pith-number/4VNQU4BX4YS2QEIWJUT6YMMVCL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL/action/storage_attestation","attest_author":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL/action/author_attestation","sign_citation":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL/action/citation_signature","submit_replication":"https://pith.science/pith/4VNQU4BX4YS2QEIWJUT6YMMVCL/action/replication_record"}},"created_at":"2026-05-18T00:59:17.526687+00:00","updated_at":"2026-05-18T00:59:17.526687+00:00"}