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Journal of Mathematical Chemistry

, Volume 52, Issue 9, pp 2322–2329 | Cite as

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

  • Francisco M. Fernández
Original Article

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.

Keywords

Avoided crossings Non-crossing rule Parameter-dependent operators Exceptional points PT symmetry 

Notes

Acknowledgments

This report has been financially supported by PIP No. 11420110100062 (Consejo Nacional de Investigaciones Cientificas y Tecnicas, República Argentina).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.División Química TeóricaINIFTA (UNLP, CCT La Plata-CONICET)La PlataArgentina

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