How to detect level crossings without looking at the spectrum

M. Bhattacharya

doi:10.1119/1.2757622

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arXiv · 0705.1958

How to detect level crossings without looking at the spectrum

M. Bhattacharya

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Abstract

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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M. Bhattacharya. 2007-05-14. How to detect level crossings without looking at the spectrum. https://doi.org/10.1119/1.2757622

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