绝热近似、盖尔曼和洛定理与简并性：一个教学实例
Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example
摘要：
研究了一个由2 × 2哈密顿量描述的简单系统在微扰作用下的量子态演化。更确切地说，当初始哈密顿量是不退化的，我们检查分析的绝热近似的有效性，并验证，即使演化算子绝热开关没有限制，盖尔曼和低公式允许遵循本征态的演化。在简并情况下，对于一般的初始本征态，绝热近似（通过两种不同的限制程序获得）要么是无用的，要么是错误的，盖尔曼和洛公式不成立。我们展示了如何选择初始状态，以避免这种故障。
英文摘要：
We study a simple system described by a 2x2 Hamiltonian and the evolution of the quantum states under the influence of a perturbation. More precisely, when the initial Hamiltonian is not degenerate,we check analytically the validity of the adiabatic approximation and verify that, even if the evolution operator has no limit for adiabatic switchings, the Gell-Mann and Low formula allows to follow the evolution of eigenstates. In the degenerate case, for generic initial eigenstates, the adiabatic approximation (obtained by two different limiting procedures) is either useless or wrong, and the Gell-Mann and Low formula does not hold. We show how to select initial states in order to avoid such failures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
