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        "quote": "我们现在假定每个物理系统都对应一个可分的希尔伯特空间，表示该系统所有可能的状态。该希尔伯特空间可以是有限维的，例如光子或电子的偏振态，但通常是无限维的。系统的状态由非零向量 $\\psi \\in { \\mathcal { H } } .$ 表示，但这种对应不是一一的，因为任意两个向量 $\\psi$ 和 $\\psi ^ { \\prime }$ 若通过非零复因子成比例，即 $\\psi ^ { \\prime } = \\lambda \\psi$，其中 $\\lambda \\in \\mathbb { C }$，都将被假定表示相同的状态。换言之，一个状态是向量 $[ \\psi ]$ 的一个等价类或 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:dd5a80e1-a5d1-416d-a7bc-4bf14e593eb8\" data-concept-route=\"/concept-identities#concept-dd5a80e1-a5d1-416d-a7bc-4bf14e593eb8\" id=\"first-909421c7b769a112c204-zh\">射线(ray)</u>，这些向量之间均通过比例关系相联系。一个状态可以由该类中的任意向量表示，并且通常选取一个具有单位范数 $\\| \\psi \\| = 1$ 的代表元。即使这一限制也不能唯一确定一个向量来表示该状态，因为任何其他满足 $| \\lambda | = 1$ 的向量 $\\psi ^ { \\prime } = \\lambda \\psi$ 也将满足单位范数条件。角度自由度 $\\lambda = \\mathrm { e } ^ { i c }$ 有时被称为状态向量的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:88352bef-51d3-40b4-83c8-5d8f96aae1dc\" data-concept-route=\"/concept-identities#concept-88352bef-51d3-40b4-83c8-5d8f96aae1dc\" id=\"first-4dfbeb9a4e39699c15de-zh\">相位(phase)</u>。相位仅在相对意义下才有意义；例如，$\\psi + \\mathrm { e } ^ { i c } \\phi$ 通常是与 $\\psi + \\phi$ 不同的状态，但 $\\mathsf { e } ^ { i c } ( \\psi + \\phi )$ 则不是。",
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