On the crossing of the energy levels of a parameter-dependent   quantum-mechanical Hamiltonian
  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. 
Francisco M. Fern\'andez
quant-ph