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            "text": "单自由度谐振子的相干态由位移算符作用于真空态得到：\n\n$$\n| \\alpha \\rangle = D (\\alpha) | 0 \\rangle = e ^ {\\alpha a ^ {\\dagger} - \\overline {{\\alpha}} a} | 0 \\rangle\n$$\n\n",
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          },
          {
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            "summary": "作者先从谐振子真空态出发，以位移算符定义相干态；随后展开为数态级数，验证它是湮灭算符的本征态，并说明参数 $\\alpha$ 给出位置与动量的期望值。",
            "conditions": "讨论单自由度谐振子；$|0\\rangle$ 是真空态，$a$ 是湮灭算符，$D(\\alpha)$ 为位移算符。该节还指出海森堡群作用不是谐振子哈密顿量的对称性。",
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            "text": "先读第 23.1 节真空态经位移算符得到相干态的定义，再读其数态展开和本征态性质；随后看期望值公式，理解 $\\alpha$ 如何表示位置与动量的取值中心。",
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          "已收录材料集中于第 23.1 节，没有穷尽相干态在全书中的其他构造与应用。"
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