{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
  "labels": {
    "zh-CN": "期望值",
    "en": "expectation value"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "expectation values"
    }
  ],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "d1157cb4a1aaa4c675e2c974a59990860b4c1e2191f7646a3bb5fd3914ae50b0",
  "occurrences": [
    {
      "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
      "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-expectation-value",
      "chapter": "7",
      "section": "7.2",
      "offset": 5540,
      "range": [
        15751,
        16106
      ],
      "source_revision": "af42ca8c868bc2cdc5dca3ef8a46b1cd266fae227aaba16f410d9185fd6d5068",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "期望值(expectation value)",
      "context": {
        "range": [
          15701,
          16236
        ],
        "quote": "量子系统处于任意态 $|\\psi\\rangle$ 时，可观测量 $A$ 未必有确定值，但仍可计算其[<u id=\"concept-7-expectation-value\" class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/expectation-value\" data-concept-id=\"concept-7-expectation-value\" data-concept-identity=\"urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759\" data-concept-route=\"/concept-identities#concept-57eeacec-5920-4133-83e9-8b4cd48bf759\">期望值(expectation value)</u>](../../../../../concepts/quantum-mechanics/expectation-value)。取由 $H$ 的正交特征向量构成的一组基，将各特征值按其出现概率加权求和。对于 $A=S_j$，用 $S_j$ 的特征向量展开态，可得",
        "quote_sha256": "e2e11eb6dc7ca1ffc7dd43459221231d330cc1b1875f2ee28b26eb3fdce0854d",
        "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-7f4556f0ab7e4b7391c14a98"
    },
    {
      "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/03-the-heisenberg-picture",
      "anchor": "concept-7-3-expectation-value",
      "chapter": "7",
      "section": "7.3",
      "offset": 4294,
      "range": [
        12498,
        12857
      ],
      "source_revision": "5f8a0b2cc9d948646265bae64b9542fa1540f818465f92fddd4b78fdfc0c7c90",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "期望值(expectation value)",
      "context": {
        "range": [
          12075,
          12924
        ],
        "quote": "下标 $H$ 表示采用海森堡绘景来处理时间依赖性。容易看出，两种绘景中可观测量的[<u id=\"concept-7-3-eigenvalue\" class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/eigenvalue\" data-concept-id=\"concept-7-3-eigenvalue\" data-concept-identity=\"urn:uuid:76dd2837-afb9-4545-a9b3-37d92e61b023\" data-concept-route=\"/concept-identities#concept-76dd2837-afb9-4545-a9b3-37d92e61b023\">特征值(eigenvalue)</u>](../../../../../concepts/linear-algebra/eigenvalue)和[<u id=\"concept-7-3-expectation-value\" class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/expectation-value\" data-concept-id=\"concept-7-3-expectation-value\" data-concept-identity=\"urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759\" data-concept-route=\"/concept-identities#concept-57eeacec-5920-4133-83e9-8b4cd48bf759\">期望值(expectation value)</u>](../../../../../concepts/quantum-mechanics/expectation-value)完全相同：",
        "quote_sha256": "9ae77c38d811181be36535cd50539be6a37b9605a3b15833b757ee0d222e16e0",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-07/03-the-heisenberg-picture",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-7cfc373a5d2f0913dbbfa8f3"
    },
    {
      "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-07/03-the-heisenberg-picture",
      "anchor": "concept-7-3-expectation-value",
      "chapter": "7",
      "section": "7.3",
      "offset": 4761,
      "range": [
        12128,
        12483
      ],
      "source_revision": "2134547383964d76a976c6c9c25db57afd0f18f358f6c08e86ad956e1e5932bf",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "expectation values",
      "context": {
        "range": [
          11604,
          12580
        ],
        "quote": "The subscript $H$ indicates the Heisenberg-picture choice for treating time dependence. It is easy to see that the observable quantities—the [<u id=\"concept-7-3-eigenvalue\" class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/eigenvalue\" data-concept-id=\"concept-7-3-eigenvalue\" data-concept-identity=\"urn:uuid:76dd2837-afb9-4545-a9b3-37d92e61b023\" data-concept-route=\"/concept-identities#concept-76dd2837-afb9-4545-a9b3-37d92e61b023\">eigenvalues</u>](../../../../../concepts/linear-algebra/eigenvalue) and [<u id=\"concept-7-3-expectation-value\" class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/expectation-value\" data-concept-id=\"concept-7-3-expectation-value\" data-concept-identity=\"urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759\" data-concept-route=\"/concept-identities#concept-57eeacec-5920-4133-83e9-8b4cd48bf759\">expectation values</u>](../../../../../concepts/quantum-mechanics/expectation-value)—are identical in the two pictures:",
        "quote_sha256": "0e8d4075977e8a81729e9617c51ea5f5f77fff126a79b1604a1df84ea37a116c",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/03-the-heisenberg-picture",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-4bf57dba3db3ed1781fe11ef"
    },
    {
      "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space",
      "anchor": "source-7-4-quotient-space",
      "chapter": "7",
      "section": "7.4",
      "offset": 2288,
      "range": [
        10368,
        10644
      ],
      "source_revision": "dece3546a425ea2c52b709472898bb8128e5d5d751614a636ab79e1e1bbfe61c",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "期望值(expectation value)",
      "context": {
        "range": [
          8996,
          11172
        ],
        "quote": null,
        "quote_sha256": "393256bdf68f6916b07aaad6279e18f04be89d779ecaf45aea0b13d8cf50e663",
        "environment": null,
        "excerpt_omitted": true
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-1007f8a6e8f3fdf8d24cfa1f"
    },
    {
      "concept_id": "urn:uuid:57eeacec-5920-4133-83e9-8b4cd48bf759",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space",
      "anchor": "first-f4a8739c294321ab2ef9-en",
      "chapter": "7",
      "section": "7.4",
      "offset": 2407,
      "range": [
        9820,
        10092
      ],
      "source_revision": "56ee7f1727deaa19e151a716a8ad06b4eb7d62437a0e4e97e582b9d242bc09a3",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "expectation values",
      "context": {
        "range": [
          8322,
          10786
        ],
        "quote": null,
        "quote_sha256": "0b96e8ba182265b17db63f81901d54cbdb7e69c6d080ece41f98fb362cf8b690",
        "environment": null,
        "excerpt_omitted": true
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-f4ce76389125630b1a4761dd"
    }
  ],
  "registered_positions": [
    {
      "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": "期望值",
      "english": "expectation value",
      "offset": 4292
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/03-the-heisenberg-picture",
      "lang": "zh-CN",
      "section": "7.3",
      "signal": "term-mark",
      "label": "期望值",
      "english": "expectation value",
      "offset": 3011
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/04-complex-projective-space",
      "lang": "zh-CN",
      "section": "7.4",
      "signal": "term-mark",
      "label": "期望值",
      "english": "expectation value",
      "offset": 1473
    },
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-07/03-the-heisenberg-picture",
      "lang": "en",
      "section": "7.3",
      "signal": "term-mark",
      "label": "expectation values",
      "english": "expectation values",
      "offset": 3478
    },
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-07/04-complex-projective-space",
      "lang": "en",
      "section": "7.4",
      "signal": "term-mark",
      "label": "expectation values",
      "english": "expectation values",
      "offset": 1557
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-7f4556f0ab7e4b7391c14a98",
    "occ-7cfc373a5d2f0913dbbfa8f3",
    "occ-4bf57dba3db3ed1781fe11ef",
    "occ-1007f8a6e8f3fdf8d24cfa1f",
    "occ-f4ce76389125630b1a4761dd"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 5,
    "located_occurrences": 5,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "df1bd218e0675d31c1a7e5ade55d686dd9cd38a2bd82f28532893f3a1d6ff0be",
  "optional_enrichments": []
}
