{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:27GYWZZ7Y7CXT5E66EM4YGDP6N","short_pith_number":"pith:27GYWZZ7","schema_version":"1.0","canonical_sha256":"d7cd8b673fc7c579f49ef119cc186ff36e71ce09060154cc6dc98b1e47ac801c","source":{"kind":"arxiv","id":"1608.08256","version":2},"attestation_state":"computed","paper":{"title":"Aspects of Perturbation theory in Quantum Mechanics: The BenderWu Mathematica package","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","quant-ph"],"primary_cat":"hep-th","authors_text":"Mithat \\\"Unsal, Tin Sulejmanpasic","submitted_at":"2016-08-29T21:23:32Z","abstract_excerpt":"We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu, and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use Mathematica package we call BenderWu. Our package e"},"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":"1608.08256","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-29T21:23:32Z","cross_cats_sorted":["hep-lat","quant-ph"],"title_canon_sha256":"c5921e73705a759cb977d367e92f3b10e305867b1fa3f1cf4580c8714cd5d0c3","abstract_canon_sha256":"10d999a926dd615b5cbee4795d8a132b3827aa571211e4986d00b7f18e9cbd8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:10.316594Z","signature_b64":"nFrfupXXI/I+pLYYLGlmMT0btveuojQ219yfTwG3v4lo+YxOO9uHftM8EuTRGhkp/ZkUoPRBwW7uaIZ8XUYlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7cd8b673fc7c579f49ef119cc186ff36e71ce09060154cc6dc98b1e47ac801c","last_reissued_at":"2026-05-18T01:05:10.315900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:10.315900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Aspects of Perturbation theory in Quantum Mechanics: The BenderWu Mathematica package","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","quant-ph"],"primary_cat":"hep-th","authors_text":"Mithat \\\"Unsal, Tin Sulejmanpasic","submitted_at":"2016-08-29T21:23:32Z","abstract_excerpt":"We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu, and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use Mathematica package we call BenderWu. Our package e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08256","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.08256","created_at":"2026-05-18T01:05:10.316016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.08256v2","created_at":"2026-05-18T01:05:10.316016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08256","created_at":"2026-05-18T01:05:10.316016+00:00"},{"alias_kind":"pith_short_12","alias_value":"27GYWZZ7Y7CX","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"27GYWZZ7Y7CXT5E6","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"27GYWZZ7","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2602.20576","citing_title":"Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics","ref_index":44,"is_internal_anchor":true},{"citing_arxiv_id":"2604.05878","citing_title":"Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence","ref_index":140,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05878","citing_title":"Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence","ref_index":140,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N","json":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N.json","graph_json":"https://pith.science/api/pith-number/27GYWZZ7Y7CXT5E66EM4YGDP6N/graph.json","events_json":"https://pith.science/api/pith-number/27GYWZZ7Y7CXT5E66EM4YGDP6N/events.json","paper":"https://pith.science/paper/27GYWZZ7"},"agent_actions":{"view_html":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N","download_json":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N.json","view_paper":"https://pith.science/paper/27GYWZZ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.08256&json=true","fetch_graph":"https://pith.science/api/pith-number/27GYWZZ7Y7CXT5E66EM4YGDP6N/graph.json","fetch_events":"https://pith.science/api/pith-number/27GYWZZ7Y7CXT5E66EM4YGDP6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N/action/storage_attestation","attest_author":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N/action/author_attestation","sign_citation":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N/action/citation_signature","submit_replication":"https://pith.science/pith/27GYWZZ7Y7CXT5E66EM4YGDP6N/action/replication_record"}},"created_at":"2026-05-18T01:05:10.316016+00:00","updated_at":"2026-05-18T01:05:10.316016+00:00"}