{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:d07b8252-8aa0-41c2-a5b3-a8bec45db852", "labels": { "zh-CN": "可观测量", "en": "observable" }, "alternative_labels": [ { "lang": "en", "value": "observables" } ], "scope_note": "", "identity_status": "active", "identity_revision": "0fde4131445ab0b673fe704c44026df8438dd9365543b2bea130ce6236014b1b", "occurrences": [ { "concept_id": "urn:uuid:d07b8252-8aa0-41c2-a5b3-a8bec45db852", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "zh-CN", "route": "zh/chapter-14/01-basic-concepts", "anchor": "first-c5a94a7805820963224f-zh", "chapter": "14", "section": "14.1", "offset": 9184, "range": [ 15506, 15741 ], "source_revision": "aa7ae5d33878e4eddbd8c7943c808eda392dd1072d2000abb456f9ac1793e9dd", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "可观测量(observable)", "context": { "range": [ 15497, 16183 ], "quote": "在经典力学中，物理可观测量(observable)指的是位置、动量、能量或角动量等量，它们是实数或实多分量对象。在量子力学中，可观测量由态希尔伯特空间上的自伴算符表示。我们首先考虑$A$是厄米算符（有界且连续）的情形。若相应的厄米算符$A$是完备的，使得存在由特征向量${ | \\psi _ { 1 } \\rangle } , { | \\psi _ { 2 } \\rangle } , . . .$构成的正交标准基，则称这样的可观测量为完备可观测量(complete observable)。使得", "quote_sha256": "7950be95be1c44d7ba5d166a676e2b4d71ade1259ae24d98e14aa5230d788eea", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "en/chapter-14/01-basic-concepts", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-914bb3bfc4391769585ee16c" }, { "concept_id": "urn:uuid:d07b8252-8aa0-41c2-a5b3-a8bec45db852", "book_id": "szekeres", "edition_id": "source-snapshot-bc3404156f6e", "lang": "en", "route": "en/chapter-14/01-basic-concepts", "anchor": "first-4f6956ccc70e62d5b6f9-en", "chapter": "14", "section": "14.1", "offset": 14077, "range": [ 19928, 20158 ], "source_revision": "5ffc1a138ecca9c924f0557a73a687627be309ac35b887823d07e23731a53f3b", "source_category": "original_transcription", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "observables", "context": { "range": [ 19896, 21023 ], "quote": "In classical mechanics,physical observables refer to quantities such as position, momentum, energy or angular momentum, which are real numbers or real multicomponented objects. In quantum mechanics observables are represented by self-adjoint operators on the Hilbert space of states. We first consider the case where $A$ is a hermitian operator (bounded and continuous). Such an observable is said to be complete if the corresponding hermitian operator $A$ is complete, so that there is an orthonormal basis made up of eigenvectors ${ | \\psi _ { 1 } \\rangle } , { | \\psi _ { 2 } \\rangle } , . . .$ . such that", "quote_sha256": "01f4dcdb62625e523512d51d7c0f2359e4e5335bd74acd3e61cc7f0645286920", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "zh/chapter-14/01-basic-concepts", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-eab161250a116a9cee497467" }, { "concept_id": "urn:uuid:d07b8252-8aa0-41c2-a5b3-a8bec45db852", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/07-eigenvalues-and-eigenvectors", "anchor": "first-c7877353e297ad512e88-zh", "chapter": "4", "section": "4.7", "offset": 3806, "range": [ 10979, 11285 ], "source_revision": "8286f925db1403c9f914ba0ff3d431f42dd161d85f19656a9a0833745e908bd2", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "可观测量(observable)", "context": { "range": [ 10549, 11735 ], "quote": "这里的[谱定理(spectral theorem)](../../../../../concepts/linear-algebra/spectral-theorem)讨论有限维向量空间与矩阵；不过，对无限维态空间上的自伴算符也有类似结论。在量子力学中，这类定理至关重要：若 $L$ 是一个[可观测量(observable)](../../../../../concepts/quantum-mechanics/quantum-observable)，其特征向量就是态空间中该可观测量取值确定的态，而这些数值就是特征值。谱定理还说明，可以用该可观测量为态空间选取一组特殊的[正交标准基(orthonormal basis)](../../../../../concepts/linear-algebra/basis)，即由归一化特征向量构成的基。", "quote_sha256": "6e419e5855e050b28129215a0c5f4d5de4be1bd18dc3ca7ab6071f9f7574e678", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-04/07-eigenvalues-and-eigenvectors", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; 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