{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:85694223-0c9f-4798-a693-c9ae294130f3", "labels": { "zh-CN": "相空间", "en": "phase space" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "e8d7965b08e68715f6d65530b1f01a530ea87125a0ff15b0b4ab4d44460c4487", "occurrences": [ { "concept_id": "urn:uuid:85694223-0c9f-4798-a693-c9ae294130f3", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-16/05-classical-mechanics", "anchor": "first-8c18c8afa671277219b5-zh", "chapter": "16", "section": "16.5", "offset": 36661, "range": [ 44441, 44676 ], "source_revision": "aac6045c8f792acfb5c9989193835b417610f4c945fe5f70074b9b0c3fb0e939", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "相空间(phase space)", "context": { "range": [ 44399, 45113 ], "quote": "由 $M$ 上的动量 1-形式构成的余切丛 $T ^ { * } M$，称为系统的 相空间(phase space)。坐标 $p _ { i }$ 与 $\\dot { q } ^ { j }$ 由式 (16.30) 相联系，因此速度分量可以用广义动量表示，$\\dot { q } ^ { j } = g ^ { j k } p _ { k }$，其中 $g ^ { j k } g _ { k i } = \\delta _ { i : } ^ { j }$，而拉格朗日方程 式 (16.29) 可以写成", "quote_sha256": "22d876eabd3d0f591b11799234a5651e9b0290ce896643cf7ecae636e225c7e0", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-16/05-classical-mechanics", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-466d67d955c37169523d2715" }, { "concept_id": "urn:uuid:85694223-0c9f-4798-a693-c9ae294130f3", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-16/05-classical-mechanics", "anchor": "first-8c18c8afa671277219b5-en", "chapter": "16", "section": "16.5", "offset": 48267, "range": [ 55576, 55806 ], "source_revision": "6ba31cc0cea910b2bb1780c9e846e4e265229202d450afd615e6b7053ad533bb", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "phase space", "context": { "range": [ 55484, 56381 ], "quote": "the cotangent bundle $T ^ { * } M$ , consisting of momentum 1-forms on $M$, is known as the phase space of the system. The coordinates $p _ { i }$ and $\\dot { q } ^ { j }$ are related by Eq. (16.30), so that velocity components can be expressed in terms ofgeneralized momenta, $\\dot { q } ^ { j } = g ^ { j k } p _ { k }$ where $g ^ { j k } g _ { k i } = \\delta _ { i : } ^ { j }$ , and Lagrange’s equations Eq. (16.29) can be written", "quote_sha256": "fb5b3499210f477544d7aad86a2387a4997c808a4591a4a189c147e7ad07adb4", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-16/05-classical-mechanics", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-f7b9c01237b6db675783152a" }, { "concept_id": "urn:uuid:85694223-0c9f-4798-a693-c9ae294130f3", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/02-basic-principles-of-quantum-mechanics", "anchor": "first-3ed50b2c89c22e69f977-zh", "chapter": "1", "section": "1.2", "offset": 608, "range": [ 10756, 10991 ], "source_revision": "99f4970c9db6d9ce77b4a64acccb2993c200b986fea023cc4d14e79b6881b92e", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "相空间(phase space)", "context": { "range": [ 10741, 11669 ], "quote": "在经典物理学中，系统的状态由“相空间(phase space)”中的一个点表示。相空间也可以看作运动方程的解空间；若以初始值数据为参数，则它也可视为坐标与动量构成的空间。可观测量就是定义在这个空间上的函数（例如坐标和动量的函数）。其中有一个特殊的可观测量是能量，即哈密顿量(Hamiltonian)；它通过哈密顿方程(Hamilton’s equations)决定状态如何随时间演化。", "quote_sha256": "d3667f1ff469b567ed399bbd999f31a4af74f0c7c0c85bb7673708331f5194fb", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-01/02-basic-principles-of-quantum-mechanics", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-e0761a09ccafb4baf7ca8b03" } ], "registered_positions": [ { "route": "en/chapter-16/05-classical-mechanics", "lang": "en", "section": "16.5", "signal": "term-mark", "label": "phase space", "english": "phase space", "offset": 45975 }, { "route": "zh/chapter-16/05-classical-mechanics", "lang": "zh-CN", "section": "16.5", "signal": "term-mark", "label": "相空间", "english": "phase space", "offset": 34369 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/02-basic-principles-of-quantum-mechanics", "lang": "zh-CN", "section": "1.2", "signal": "term-mark", "label": "相空间", "english": "phase space", "offset": 608 } ], "statements": [], "resolved_references": [ { "raw": "href=\"#equation-16-30\"", "href": "#equation-16-30", "range": [ 44719, 44741 ], "relation": "references", "target_route": "zh/chapter-16/05-classical-mechanics", "target_anchor": "equation-16-30", "resolved": true, "reason": null, "source_revision": "aac6045c8f792acfb5c9989193835b417610f4c945fe5f70074b9b0c3fb0e939", "source_route": "zh/chapter-16/05-classical-mechanics", "occurrence_id": "occ-466d67d955c37169523d2715" }, { "raw": "href=\"#equation-16-29\"", "href": "#equation-16-29", "range": [ 44980, 45002 ], "relation": "references", "target_route": "zh/chapter-16/05-classical-mechanics", "target_anchor": "equation-16-29", "resolved": true, "reason": null, "source_revision": "aac6045c8f792acfb5c9989193835b417610f4c945fe5f70074b9b0c3fb0e939", "source_route": "zh/chapter-16/05-classical-mechanics", "occurrence_id": "occ-466d67d955c37169523d2715" }, { "raw": "href=\"#equation-16-30\"", "href": "#equation-16-30", "range": [ 55893, 55915 ], "relation": "references", "target_route": "en/chapter-16/05-classical-mechanics", "target_anchor": "equation-16-30", "resolved": true, "reason": null, "source_revision": "6ba31cc0cea910b2bb1780c9e846e4e265229202d450afd615e6b7053ad533bb", "source_route": "en/chapter-16/05-classical-mechanics", "occurrence_id": "occ-f7b9c01237b6db675783152a" }, { "raw": "href=\"#equation-16-29\"", "href": "#equation-16-29", "range": [ 56236, 56258 ], "relation": "references", "target_route": "en/chapter-16/05-classical-mechanics", "target_anchor": "equation-16-29", "resolved": true, "reason": null, "source_revision": "6ba31cc0cea910b2bb1780c9e846e4e265229202d450afd615e6b7053ad533bb", "source_route": "en/chapter-16/05-classical-mechanics", "occurrence_id": "occ-f7b9c01237b6db675783152a" } ], "reading_order": [ "occ-466d67d955c37169523d2715", "occ-f7b9c01237b6db675783152a", "occ-e0761a09ccafb4baf7ca8b03" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 3, "located_occurrences": 3, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "0299cd7c860a396b7ba45e34c4e9cbe2fee4f9be5d67110d9d0b6fa8a4024d6b", "optional_enrichments": [] }