如何在不查看频谱的情况下检测电平交叉
How to detect level crossings without looking at the spectrum
摘要：
我们提醒读者，可以判断矩阵的两个或多个特征值是否相等，而无需计算特征值。然后，我们使用这个属性来检测（避免）交叉的量子哈密顿矩阵表示的频谱。这种方法提供了一个教学介绍（避免）交叉，是能够处理现实的哈密顿分析，并提供了一种方式来可视化交叉，有时优于所提供的频谱。我们用Breit-Rabi哈密顿量描述了均匀磁场中基态氢原子的超精细塞曼结构。
英文摘要：
We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians representable by matrices. This approach provides a pedagogical introduction to (avoided) crossings, is capable of handling realistic Hamiltonians analytically, and offers a way to visualize crossings which is sometimes superior to that provided by the spectrum. We illustrate the method using the Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground state hydrogen atom in a uniform magnetic field.
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