{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:8138ecc5-6158-4786-afec-925599c67b25", "labels": { "zh-CN": "旋磁比", "en": "gyromagnetic ratio" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "21a48540ae4fa800f77b5ab2781ee1008f0adfdf37b56451bb1ee8d9ffdeef5d", "occurrences": [ { "concept_id": "urn:uuid:8138ecc5-6158-4786-afec-925599c67b25", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-03/03-dynamics-of-a-two-state-system", "anchor": "first-e018b22fe6d6d650c1fe-zh", "chapter": "3", "section": "3.3", "offset": 6699, "range": [ 14073, 14393 ], "source_revision": "bf7bed127428e26ee378fb9b0fdf940a9534adebb0b55c3a053bcb959f95722e", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "旋磁比(gyromagnetic ratio)", "context": { "range": [ 13983, 14583 ], "quote": "其中，$B_j$ 是磁场的分量；物理常数包括旋磁比(gyromagnetic ratio) $g$、电荷 $e$、质量 $m$ 和光速 $c$。令 $h_j=\\frac{ge}{4mc}B_j$，代入上式中的 $U(t)$，即可得到该系统的时间演化。若磁场沿第 3 方向，即 $B_1=B_2=0$，则两个能量确定的态（$|+\\frac{1}{2}\\rangle$ 和 $|-\\frac{1}{2}\\rangle$；回忆一下，能量就是哈密顿算符的特征值）之间的能量差为：", "quote_sha256": "1996d1b7c814b6073d854877ae6be90883e0587034e3e79aa43b24a7b078bfd4", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-03/03-dynamics-of-a-two-state-system", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-cf6c2417ff1939c756ad6641" }, { "concept_id": "urn:uuid:8138ecc5-6158-4786-afec-925599c67b25", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-03/03-dynamics-of-a-two-state-system", "anchor": "first-e018b22fe6d6d650c1fe-en", "chapter": "3", "section": "3.3", "offset": 6764, "range": [ 13381, 13696 ], "source_revision": "fa8dc6f1abe776e62ef8b602a476972f2cd33199732383a20aabeb58fb3bed8c", "source_category": "original_transcription", "review_status": "ai-transcription-compared", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "gyromagnetic ratio", "context": { "range": [ 13229, 14112 ], "quote": "Here $B_j$ are the components of the magnetic field. The physical constants are the gyromagnetic ratio $g$, the electric charge $e$, the mass $m$, and the speed of light $c$. Taking $h_j=\\frac{ge}{4mc}B_j$ in the expression for $U(t)$ above gives the time evolution of the system. If the magnetic field points in the 3-direction, so that $B_1=B_2=0$, the two states with definite energies ($|+\\frac{1}{2}\\rangle$ and $|-\\frac{1}{2}\\rangle$; recall that energy is the eigenvalue of the Hamiltonian) differ in energy by:", "quote_sha256": "7f5c49f3b085141a8fa054fa849986593f326307d09f9c04f51844bcbd302578", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-03/03-dynamics-of-a-two-state-system", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-827009d65a2f3c82a3d4eff8" }, { "concept_id": "urn:uuid:8138ecc5-6158-4786-afec-925599c67b25", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "anchor": "concept-7-gyromagnetic-ratio", "chapter": "7", "section": "7.2", "offset": 9680, "range": [ 19891, 20132 ], "source_revision": "af42ca8c868bc2cdc5dca3ef8a46b1cd266fae227aaba16f410d9185fd6d5068", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "旋磁比(gyromagnetic ratio)", "context": { "range": [ 19848, 20214 ], "quote": "其中，$-e$ 是电荷，$c$ 是光速，$m$ 是粒子质量。无量纲常数 $g$ 称为[旋磁比(gyromagnetic ratio)](../../../../../concepts/quantum-mechanics/gyromagnetic-ratio)；对电子约为 2，对质子约为 5.6。", "quote_sha256": "86d0dd21f4ae83abddb674e92cdd672417110711ea26426b6e0c4bc127230c5f", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-d8841fb03bafc1bb857d53de" }, { "concept_id": "urn:uuid:8138ecc5-6158-4786-afec-925599c67b25", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "anchor": "first-eaf57b445651d135ec4a-en", "chapter": "7", "section": "7.2", "offset": 12046, "range": [ 21367, 21569 ], "source_revision": "2f4e030ded93d226da1b050014630cb67a384fcab12bb0f30e051144b3d12eec", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "gyromagnetic ratio", "context": { "range": [ 21238, 21696 ], "quote": "Here $-e$ is the electric charge, $c$ the speed of light, and $m$ the particle mass. The dimensionless constant $g$, called the [gyromagnetic ratio](../../../../../concepts/quantum-mechanics/gyromagnetic-ratio), is approximately 2 for an electron and about 5.6 for a proton.", "quote_sha256": "6795405c0a55110da7dc99a3d6f35b5a272e9b4bcf7f0d64f70b0a0e76f6ccd5", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-67d77ca8e47b994821833463" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-03/03-dynamics-of-a-two-state-system", "lang": "en", "section": "3.3", "signal": "term-mark", "label": "gyromagnetic ratio", "english": "gyromagnetic ratio", "offset": 5438 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-03/03-dynamics-of-a-two-state-system", "lang": "zh-CN", "section": "3.3", "signal": "term-mark", "label": "旋磁比", "english": "gyromagnetic ratio", "offset": 5044 }, { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "en", "section": "7.2", "signal": "term-mark", "label": "gyromagnetic ratio", "english": "gyromagnetic ratio", "offset": 9964 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "zh-CN", "section": "7.2", "signal": "term-mark", "label": "旋磁比", "english": "gyromagnetic ratio", "offset": 7652 } ], "statements": [], "resolved_references": [], "reading_order": [ "occ-cf6c2417ff1939c756ad6641", "occ-827009d65a2f3c82a3d4eff8", "occ-d8841fb03bafc1bb857d53de", "occ-67d77ca8e47b994821833463" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 4, "located_occurrences": 4, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "ca796bbde8508cb231b8f46a63e0f3e92887f43159d5228cb9554621277d01c5", "optional_enrichments": [] }