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        "quote": "这里的[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/spectral-theorem\" data-concept-identity=\"urn:uuid:1a675aab-c7ae-434f-b33d-dbac51890000\" data-concept-route=\"/concept-identities#concept-1a675aab-c7ae-434f-b33d-dbac51890000\" id=\"first-65a47865eb101c002a18-zh\">谱定理(spectral theorem)</u>](../../../../../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[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/quantum-observable\" data-concept-identity=\"urn:uuid:d07b8252-8aa0-41c2-a5b3-a8bec45db852\" data-concept-route=\"/concept-identities#concept-d07b8252-8aa0-41c2-a5b3-a8bec45db852\" id=\"first-c7877353e297ad512e88-zh\">可观测量(observable)</u>](../../../../../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[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/basis\" data-concept-identity=\"urn:uuid:dabe32db-8d84-4c17-9eeb-583f0609a265\" data-concept-route=\"/concept-identities#concept-dabe32db-8d84-4c17-9eeb-583f0609a265\">正交标准基(orthonormal basis)</u>](../../../../../concepts/linear-algebra/basis)，即由归一化特征向量构成的基。",
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