{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:87bf0817-1c0e-449a-aab5-70e73e7d9c72",
  "labels": {
    "zh-CN": "动量算符",
    "en": "Momentum operators"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "a26a3aa7addcacb19cf3fd844d6bcaee0e7ab403a912c385babb8d2e8340de0b",
  "occurrences": [
    {
      "concept_id": "urn:uuid:87bf0817-1c0e-449a-aab5-70e73e7d9c72",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-10/02-translations-in-time-and-space",
      "anchor": "first-142e8da5eb4195114da7-zh",
      "chapter": "10",
      "section": "10.2",
      "offset": 1232,
      "range": [
        7866,
        8239
      ],
      "source_revision": "16dc94d716262f91efe34303ec64a9020752f19643d817632122fb8cb8c13325",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "definition",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-10/02-translations-in-time-and-space",
          "lang": "zh-CN",
          "section": "10.2",
          "signal": "named-definition",
          "label": "动量算符",
          "english": "",
          "offset": 1162
        }
      },
      "label": "> [!definition] 定义（动量算符）",
      "context": {
        "range": [
          7866,
          8239
        ],
        "quote": "\n\n> [!definition] 定义（动量算符）\n> 对于状态空间为 $\\mathcal { H } = L ^ { 2 } ( \\mathbf { R } ^ { 3 } )$、由位置变量 $q _ { 1 } , q _ { 2 } , q _ { 3 }$ 的复值函数给出的量子系统，动量算符 $P _ { 1 } , P _ { 2 } , P _ { 3 }$ 定义为\n>\n> $$\n> P _ {1} = - i \\hbar \\frac {\\partial}{\\partial q _ {1}}, P _ {2} = - i \\hbar \\frac {\\partial}{\\partial q _ {2}}, P _ {3} = - i \\hbar \\frac {\\partial}{\\partial q _ {3}}\n> $$\n",
        "quote_sha256": "6d596c9aa6c109d13f917c0b5d49726a9bc7facb851b0aa6881107fe0dc91300",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-10/02-translations-in-time-and-space",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-d4b2c31b88362def38007170"
    },
    {
      "concept_id": "urn:uuid:87bf0817-1c0e-449a-aab5-70e73e7d9c72",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-10/02-translations-in-time-and-space",
      "anchor": "first-e6f103383e85fa6de992-en",
      "chapter": "10",
      "section": "10.2",
      "offset": 2279,
      "range": [
        8072,
        8557
      ],
      "source_revision": "919cf715828ba1820c6121ed1f6a6b825cec4c35ec85fd6acb142f5b02fae3ec",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-10/02-translations-in-time-and-space",
          "lang": "en",
          "section": "10.2",
          "signal": "named-theorem",
          "label": "Momentum operators",
          "english": "Momentum operators",
          "offset": 2209
        }
      },
      "label": "> [!theorem] Definition (Momentum operators)",
      "context": {
        "range": [
          8072,
          8557
        ],
        "quote": "\n\n> [!theorem] Definition (Momentum operators)\n> For a quantum system with state space $\\mathcal { H } = L ^ { 2 } ( \\mathbf { R } ^ { 3 } )$ given by complex-valued functions of position variables $q _ { 1 } , q _ { 2 } , q _ { 3 }$ momentum operators $P _ { 1 } , P _ { 2 } , P _ { 3 }$ are defined by\n>\n> $$\n> P _ {1} = - i \\hbar \\frac {\\partial}{\\partial q _ {1}}, P _ {2} = - i \\hbar \\frac {\\partial}{\\partial q _ {2}}, P _ {3} = - i \\hbar \\frac {\\partial}{\\partial q _ {3}}\n> $$\n",
        "quote_sha256": "7a346db4fc136c85532a55102b32e2958ec6bbeb37bda971aba7a936b51b7add",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-10/02-translations-in-time-and-space",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-7a256f5f1a8118141c45d1db"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-10/02-translations-in-time-and-space",
      "lang": "en",
      "section": "10.2",
      "signal": "named-theorem",
      "label": "Momentum operators",
      "english": "Momentum operators",
      "offset": 2209
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-10/02-translations-in-time-and-space",
      "lang": "zh-CN",
      "section": "10.2",
      "signal": "named-definition",
      "label": "动量算符",
      "english": "",
      "offset": 1162
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-d4b2c31b88362def38007170",
    "occ-7a256f5f1a8118141c45d1db"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "6a53afeccbfa9b7742a8e936cdab4b72c908b7e0b0e90f24d5c10b4ad06e7f53",
  "optional_enrichments": []
}