On the crossing of the energy levels of a parameter-dependent quantum-mechanical Hamiltonian

2014/05/25 by Francisco M. Fernández, Fernández, Francisco M.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1405.6414

arxiv created 2015/04/20 · arxiv updated 2015/04/22

Abstract

The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them shows the close relationship between avoided crossings and exceptional points.

Related

• Avoided crossings of energy levels in one-dimension
• Two-level adiabatic transition probability for small avoided crossings generated by tangential intersections
• Molecular dynamics at an energy-level crossing
• Absence of Energy Level Crossing for the Ground State Energy of the Rabi Model
• Non-adiabatic transitions through tilted avoided crossings