{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5RBVOETSSWG5ZD4LZXCE3BLBT6","short_pith_number":"pith:5RBVOETS","schema_version":"1.0","canonical_sha256":"ec43571272958ddc8f8bcdc44d85619fbcc422eb821520a72bb2f204f10c797a","source":{"kind":"arxiv","id":"1608.01543","version":2},"attestation_state":"computed","paper":{"title":"Hermitian Hamiltonians: Matrix versus Schr${\\\"o}$dinger's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Achint Kumar, Ankush Singhal, Mohammad Irfan, Zafar Ahmed","submitted_at":"2016-07-13T13:16:27Z","abstract_excerpt":"We draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\\\"o}dinger Hamiltonian: $H=p^2/2\\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$ does not have even one real discrete eigenvalue. Textbooks do not highlight this distinction. However, if $H$ has real discrete spectrum, by virtue of the expansion theorem, one can convert the eigenvalue problem $H\\psi_n=E_n \\psi_n$ into a matrix and get eigenvalues $E_n$ by diagonalizing the matrix. We show, that the thus obtained $E_n$ could be accurate, pr"},"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":"1608.01543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-07-13T13:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"1d6c646e425d2133edf27201ae412b9bbd68e75a25ec4214e7473494154dee79","abstract_canon_sha256":"a92134f82199cda0e7c6ccf04420df0aa72281a1a0c7780e165beb38204e7bd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:44.895964Z","signature_b64":"aswwLUgD0+/wLa5nquVWVuy5pKLxX9K39xuBYNsO4m2TWtzJ7PpQmTLGcP75c/HxoTCKC1wia1ov3Ft49uVJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec43571272958ddc8f8bcdc44d85619fbcc422eb821520a72bb2f204f10c797a","last_reissued_at":"2026-05-18T01:09:44.895429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:44.895429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hermitian Hamiltonians: Matrix versus Schr${\\\"o}$dinger's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Achint Kumar, Ankush Singhal, Mohammad Irfan, Zafar Ahmed","submitted_at":"2016-07-13T13:16:27Z","abstract_excerpt":"We draw attention to the fact that a Hermitian matrix is always diagonalizable and has real discrete spectrum whereas the Hermitian Schr{\\\"o}dinger Hamiltonian: $H=p^2/2\\mu+V(x)$, may not be so. For instance when $V(x)=x, x^3, -x^2$, $H$ does not have even one real discrete eigenvalue. Textbooks do not highlight this distinction. However, if $H$ has real discrete spectrum, by virtue of the expansion theorem, one can convert the eigenvalue problem $H\\psi_n=E_n \\psi_n$ into a matrix and get eigenvalues $E_n$ by diagonalizing the matrix. We show, that the thus obtained $E_n$ could be accurate, pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01543","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":"1608.01543","created_at":"2026-05-18T01:09:44.895538+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.01543v2","created_at":"2026-05-18T01:09:44.895538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01543","created_at":"2026-05-18T01:09:44.895538+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RBVOETSSWG5","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RBVOETSSWG5ZD4L","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RBVOETS","created_at":"2026-05-18T12:30:01.593930+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/5RBVOETSSWG5ZD4LZXCE3BLBT6","json":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6.json","graph_json":"https://pith.science/api/pith-number/5RBVOETSSWG5ZD4LZXCE3BLBT6/graph.json","events_json":"https://pith.science/api/pith-number/5RBVOETSSWG5ZD4LZXCE3BLBT6/events.json","paper":"https://pith.science/paper/5RBVOETS"},"agent_actions":{"view_html":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6","download_json":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6.json","view_paper":"https://pith.science/paper/5RBVOETS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.01543&json=true","fetch_graph":"https://pith.science/api/pith-number/5RBVOETSSWG5ZD4LZXCE3BLBT6/graph.json","fetch_events":"https://pith.science/api/pith-number/5RBVOETSSWG5ZD4LZXCE3BLBT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6/action/storage_attestation","attest_author":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6/action/author_attestation","sign_citation":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6/action/citation_signature","submit_replication":"https://pith.science/pith/5RBVOETSSWG5ZD4LZXCE3BLBT6/action/replication_record"}},"created_at":"2026-05-18T01:09:44.895538+00:00","updated_at":"2026-05-18T01:09:44.895538+00:00"}