{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZUTSXW5C7JV24ZHIEVF4HHCMAF","short_pith_number":"pith:ZUTSXW5C","schema_version":"1.0","canonical_sha256":"cd272bdba2fa6bae64e8254bc39c4c015fbe44c30c2b4843f7b55254e421d57b","source":{"kind":"arxiv","id":"1510.01296","version":1},"attestation_state":"computed","paper":{"title":"Investigating Student Difficulties with Dirac Notation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.ed-ph","authors_text":"Chandralekha Singh, Emily Marshman","submitted_at":"2015-10-05T19:34:04Z","abstract_excerpt":"Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notat"},"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":"1510.01296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2015-10-05T19:34:04Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"9f216adea35024672d2b263f230224507ac4bbd04d86707527068f3b6f28015a","abstract_canon_sha256":"23922348fa38e293592e1abd20b4f070d97e84458a6c59252372f43312039b43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:29.219033Z","signature_b64":"Pty/UaU9S6+2/UIabIdN0iFSjxrTVchQ5dHrDMh+owUe8LVax66We68jdpEiBaRloq8wi73HPYp248IU2BPZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd272bdba2fa6bae64e8254bc39c4c015fbe44c30c2b4843f7b55254e421d57b","last_reissued_at":"2026-05-18T01:20:29.218549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:29.218549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Investigating Student Difficulties with Dirac Notation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.ed-ph","authors_text":"Chandralekha Singh, Emily Marshman","submitted_at":"2015-10-05T19:34:04Z","abstract_excerpt":"Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced undergraduate and graduate students have with Dirac notation. We administered written free response and multiple-choice questions to students and also conducted semi-structured individual interviews with 23 students using a think-aloud protocol to obtain a better understanding of the rationale behind their responses. We find that many students struggle with Dirac notat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01296","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":"1510.01296","created_at":"2026-05-18T01:20:29.218636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01296v1","created_at":"2026-05-18T01:20:29.218636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01296","created_at":"2026-05-18T01:20:29.218636+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUTSXW5C7JV2","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUTSXW5C7JV24ZHI","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUTSXW5C","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2212.10597","citing_title":"On the representation-free formalism in quantum mechanics","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF","json":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF.json","graph_json":"https://pith.science/api/pith-number/ZUTSXW5C7JV24ZHIEVF4HHCMAF/graph.json","events_json":"https://pith.science/api/pith-number/ZUTSXW5C7JV24ZHIEVF4HHCMAF/events.json","paper":"https://pith.science/paper/ZUTSXW5C"},"agent_actions":{"view_html":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF","download_json":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF.json","view_paper":"https://pith.science/paper/ZUTSXW5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01296&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUTSXW5C7JV24ZHIEVF4HHCMAF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUTSXW5C7JV24ZHIEVF4HHCMAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF/action/storage_attestation","attest_author":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF/action/author_attestation","sign_citation":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF/action/citation_signature","submit_replication":"https://pith.science/pith/ZUTSXW5C7JV24ZHIEVF4HHCMAF/action/replication_record"}},"created_at":"2026-05-18T01:20:29.218636+00:00","updated_at":"2026-05-18T01:20:29.218636+00:00"}