{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:T3T7WWA2MGGY7W5QGWEETHGR5K","short_pith_number":"pith:T3T7WWA2","schema_version":"1.0","canonical_sha256":"9ee7fb581a618d8fdbb03588499cd1eab320a24de1d46df7c9ec5770916e5efc","source":{"kind":"arxiv","id":"1406.5875","version":1},"attestation_state":"computed","paper":{"title":"The accurate numerical solution of the Schr\\\"odinger equation with an explicitly time-dependent Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marnix Van Daele, Veerle Ledoux","submitted_at":"2014-06-23T11:48:25Z","abstract_excerpt":"We show how the highly accurate and efficient Constant Perturbation (CP) technique for steady-state Schr\\\"odinger problems can be used in the solution of time-dependent Schr\\\"odinger problems with explicitly time-dependent Hamiltonians, following a technique suggested by Ixaru in Comput. Phys. Commun. 181 (2010). By introducing a sectorwise spatial discretization using bases of accurately CP-computed eigenfunctions of carefully-chosen stationary problems, we deal with the possible highy oscillatory behaviour of the wave function while keeping the dimension of the resulting ODE system low. Also"},"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":"1406.5875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-06-23T11:48:25Z","cross_cats_sorted":[],"title_canon_sha256":"8497fb17f459079de1411859726dc00b2b3e24c2816e153351ee5d3fb14e5a91","abstract_canon_sha256":"6da895649115690d508736a124f1b042dd20034b223c84ff6cd60a7ef6cd624d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.568956Z","signature_b64":"i8mZrdQTRf7zQvlfGM+x4f9PGgUhyOfS663nZnEadrd+Ir6MAorM8ZwyODJq49iBI5gx7Lghjd8wQmOJrHQlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee7fb581a618d8fdbb03588499cd1eab320a24de1d46df7c9ec5770916e5efc","last_reissued_at":"2026-05-18T02:49:10.568408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.568408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The accurate numerical solution of the Schr\\\"odinger equation with an explicitly time-dependent Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marnix Van Daele, Veerle Ledoux","submitted_at":"2014-06-23T11:48:25Z","abstract_excerpt":"We show how the highly accurate and efficient Constant Perturbation (CP) technique for steady-state Schr\\\"odinger problems can be used in the solution of time-dependent Schr\\\"odinger problems with explicitly time-dependent Hamiltonians, following a technique suggested by Ixaru in Comput. Phys. Commun. 181 (2010). By introducing a sectorwise spatial discretization using bases of accurately CP-computed eigenfunctions of carefully-chosen stationary problems, we deal with the possible highy oscillatory behaviour of the wave function while keeping the dimension of the resulting ODE system low. Also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5875","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":"1406.5875","created_at":"2026-05-18T02:49:10.568498+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5875v1","created_at":"2026-05-18T02:49:10.568498+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5875","created_at":"2026-05-18T02:49:10.568498+00:00"},{"alias_kind":"pith_short_12","alias_value":"T3T7WWA2MGGY","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"T3T7WWA2MGGY7W5Q","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"T3T7WWA2","created_at":"2026-05-18T12:28:49.207871+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/T3T7WWA2MGGY7W5QGWEETHGR5K","json":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K.json","graph_json":"https://pith.science/api/pith-number/T3T7WWA2MGGY7W5QGWEETHGR5K/graph.json","events_json":"https://pith.science/api/pith-number/T3T7WWA2MGGY7W5QGWEETHGR5K/events.json","paper":"https://pith.science/paper/T3T7WWA2"},"agent_actions":{"view_html":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K","download_json":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K.json","view_paper":"https://pith.science/paper/T3T7WWA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5875&json=true","fetch_graph":"https://pith.science/api/pith-number/T3T7WWA2MGGY7W5QGWEETHGR5K/graph.json","fetch_events":"https://pith.science/api/pith-number/T3T7WWA2MGGY7W5QGWEETHGR5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K/action/storage_attestation","attest_author":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K/action/author_attestation","sign_citation":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K/action/citation_signature","submit_replication":"https://pith.science/pith/T3T7WWA2MGGY7W5QGWEETHGR5K/action/replication_record"}},"created_at":"2026-05-18T02:49:10.568498+00:00","updated_at":"2026-05-18T02:49:10.568498+00:00"}