{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "labels": { "zh-CN": "自旋角动量", "en": "spin angular momentum" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "ed087e84036680100d3312e05eacb257b361b98a98ab538b881c132ea2395eca", "occurrences": [ { "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-14/02-quantum-dynamics", "anchor": "first-7d8bfa0700d40e3eaff6-zh", "chapter": "14", "section": "14.2", "offset": 18610, "range": [ 25199, 25446 ], "source_revision": "169b9273ffddda2b376c5049fe82184876c85817f50c198c78c5100218af1223", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自旋角动量(spin angular momentum)", "context": { "range": [ 24440, 25574 ], "quote": "任意三个满足对易关系式 (14.25) 的算符 $L _ { 1 } , L _ { 2 } , L _ { 3 }$ 都称为 角动量算子(angular momentum operator)。若它们具有形式 $L _ { i } = \\epsilon _ { i j k } Q _ { j } P _ { k }$，则称之为 轨道角动量(orbital angular momentum)；否则称为 自旋角动量(spin angular momentum)，或其组合。若令 $J _ { i } = L _ { 1 } / \\hbar$ 和 $J ^ { 2 } = ( J _ { 1 } ) ^ { 2 } + ( J _ { 2 } ) ^ { 2 } + ( J _ { 3 } ) ^ { 2 }$，则", "quote_sha256": "938434a7075bd15a072bb52c634b62b23b210f205793dedca63fe4f317cc6853", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-14/02-quantum-dynamics", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-4cc8a7267d6588b9a2eec080" }, { "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-14/02-quantum-dynamics", "anchor": "first-7d8bfa0700d40e3eaff6-en", "chapter": "14", "section": "14.2", "offset": 23442, "range": [ 29559, 29799 ], "source_revision": "2cba95871dceac25e41bd50705d63b9d8aa14ee8e7a614492deede1f0a3da625", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "spin angular momentum", "context": { "range": [ 28703, 29961 ], "quote": "Any set of three operators $L _ { 1 } , L _ { 2 } , L _ { 3 }$ satisfying the commutation relations Eq. (14.25) are said to be angular momentum operators. If they are of the form $L _ { i } = \\epsilon _ { i j k } Q _ { j } P _ { k }$ then we term them orbital angular momentum, else they are called spin angular momentum, or a combination thereof. If we set $J _ { i } = L _ { 1 } / \\hbar$ and $J ^ { 2 } = ( J _ { 1 } ) ^ { 2 } + ( J _ { 2 } ) ^ { 2 } + ( J _ { 3 } ) ^ { 2 }$ then", "quote_sha256": "efa83037e883b75eb51da88de939e6c4627c8044e08a52eea6db727cad475551", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-14/02-quantum-dynamics", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-8f38e86eaaeaada13e90d7e0" }, { "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-34/02-solutions-of-the-pauli-equation-and-representations-of-e-3", "anchor": "first-bbddee0bc3721a136a9a-zh", "chapter": "34", "section": "34.2", "offset": 5932, "range": [ 14211, 14532 ], "source_revision": "51c84ef4d687582caaee30ac53760495d25bbbc1c467116fe66646c749fa30e1", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自旋角动量(spin angular momentum)", "context": { "range": [ 13780, 15004 ], "quote": "通常把 $\\mathbf L$ 称为[轨道角动量(orbital angular momentum)](../../../../../concepts/quantum-mechanics/orbital-angular-momentum)，$\\mathbf S$ 称为[自旋角动量(spin angular momentum)](../../../../../concepts/quantum-mechanics/spin-angular-momentum)，$\\mathbf J$ 称为[总角动量(total angular momentum)](../../../../../concepts/quantum-mechanics/total-angular-momentum)。", "quote_sha256": "ae0ce5ad6fd6cafbf075f8862b968a099b2a620da49e5a4f5a12cdda2c028011", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-34/02-solutions-of-the-pauli-equation-and-representations-of-e-3", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-263f80fbbd3fed4413100808" }, { "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-34/02-solutions-of-the-pauli-equation-and-representations-of-e-3", "anchor": "first-bbddee0bc3721a136a9a-en", "chapter": "34", "section": "34.2", "offset": 7743, "range": [ 15175, 15489 ], "source_revision": "f748916693184ebf12be265d231298eb96051a36360919ae86d0bea560f315fe", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "spin angular momentum", "context": { "range": [ 14743, 15978 ], "quote": "The standard terms are [orbital angular momentum](../../../../../concepts/quantum-mechanics/orbital-angular-momentum) for $\\mathbf L$, [spin angular momentum](../../../../../concepts/quantum-mechanics/spin-angular-momentum) for $\\mathbf S$, and [total angular momentum](../../../../../concepts/quantum-mechanics/total-angular-momentum) for $\\mathbf J$.", "quote_sha256": "0bcf9b955f88e18d8fa489782a81f671ff5b02844034288557b2fa9dd7a72558", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-34/02-solutions-of-the-pauli-equation-and-representations-of-e-3", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-76af1a1b9844e25a69562ad3" }, { "concept_id": "urn:uuid:14f530a7-cae3-4199-a129-754aeece7b1f", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-38/05-spatial-symmetries", "anchor": "xref-05-spatial-symmetries-4", "chapter": "38", "section": "38.3", "offset": 9294, "range": [ 17282, 17568 ], "source_revision": "09a614d24aa30af18566292fca84993865e67d8b9732508ac16f96a4b03abed1", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自旋角动量(spin angular momentum)", "context": { "range": [ 17098, 17696 ], "quote": "这个和来自张量积表示。其中 $\\widehat{\\mathbf L}$ 是式38.12的两份拷贝，源于空间旋转对解的诱导作用。[自旋角动量(spin angular momentum)](../../../../../concepts/quantum-mechanics/spin-angular-momentum)算符 $\\widehat{\\mathbf S}$ 则来自 $SU(2)$ 对 $\\mathbb C^2$ 因子的作用，定义为", "quote_sha256": "ddc3ba05c2e4b43fe9291068b19bfda27084c208ddb0745f65a8d342f818d6b4", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-38/05-spatial-symmetries", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; 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