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        "quote": "算符$H$称为<u class=\"concept-term\" data-concept-identity=\"urn:uuid:ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" data-concept-route=\"/concept-identities#concept-ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" id=\"first-07aec2673237abc460d2-zh\">哈密顿算子(Hamiltonian)</u>或能量算符。方程(14.13)保证所有内积都被保持，取伴随得到",
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        "quote": "Here, $H$ is a particular [<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/adjoint-operator\" data-concept-identity=\"urn:uuid:a7971b9e-8f7b-49a0-a412-0ae28a65c35b\" data-concept-route=\"/concept-identities#concept-a7971b9e-8f7b-49a0-a412-0ae28a65c35b\" id=\"first-cea3b2fa67351cb42cfb-en\">self-adjoint linear operator</u>] on $\\mathcal H$; it is the [<span id=\"first-14c43d8a9215edd8df7d-en\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/hamiltonian\" data-concept-identity=\"urn:uuid:ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" data-concept-route=\"/concept-identities#concept-ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" id=\"first-14c43d8a9215edd8df7d-quantum-en\">Hamiltonian</u>]. If $H$ is time independent, the most general such operator on $\\mathbf C^2$ has the form:",
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        "quote": "在这一系统由自旋为 $\\frac{1}{2}$ 的粒子实现时（忽略粒子的空间运动），[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/hamiltonian\" data-concept-identity=\"urn:uuid:ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" data-concept-route=\"/concept-identities#concept-ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\">哈密顿算符(Hamiltonian)</u>]为：",
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        "quote": "回顾 [3.3 节](../chapter-03/03-dynamics-of-a-two-state-system)中的讨论，我们用 $\\mathcal H=\\mathbf C^2$ 描述的自旋自由度，其动力学由[<u id=\"concept-7-hamiltonian\" class=\"concept-term\" data-concept-identity=\"urn:uuid:ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" data-concept-route=\"/concept-identities#concept-ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\">哈密顿量(Hamiltonian)</u>](../../../../../concepts/quantum-mechanics/hamiltonian)控制。",
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        "quote": "应用这些方法研究 $d$ 维量子谐振子时，我们将详细看到：当 $d=2$ 时，群 $U(2)\\subset Sp(4,\\mathbb R)$ 与[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/hamiltonian\" data-concept-identity=\"urn:uuid:ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\" data-concept-route=\"/concept-identities#concept-ce9d1194-5bd1-4a10-bd18-3aa212bbd0c7\">哈密顿算子(Hamiltonian)</u>](../../../../../concepts/quantum-mechanics/hamiltonian)对易，并作为对称群保持谐振子的能量本征子空间不变。这重现了我们在第8章中研究过的 $SU(2)\\subset U(2)$ 的全部[<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/irreducible-representation\" data-concept-identity=\"urn:uuid:4e9e2c89-0422-42cf-8762-6b5e59837ef0\" data-concept-route=\"/concept-identities#concept-4e9e2c89-0422-42cf-8762-6b5e59837ef0\">不可约表示(irreducible representation)</u>](../../../../../concepts/representation-theory/irreducible-representation)的构造。当 $d=3$ 时，对应的物理例子是三维各向同性二次中心势：旋转群以 $SO(3)$ 子群的形式作用于态空间，而 $SO(3)\\subset U(3)\\subset Sp(6,\\mathbb R)$，其中 $U(3)$ 是与哈密顿算子对易的对称子群。由此可用湮灭算符和产生算符构造角动量算符。",
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