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

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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.

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Acknowledgments

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

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  1. División Química Teórica, INIFTA (UNLP, CCT La Plata-CONICET), Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 , La Plata, Argentina

    Francisco M. Fernández

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  1. Francisco M. Fernández
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Correspondence to Francisco M. Fernández.

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Fernández, F.M. On the crossing of the energy levels of a parameter-dependent quantum-mechanical Hamiltonian. J Math Chem 52, 2322–2329 (2014). https://doi.org/10.1007/s10910-014-0386-1

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  • DOI: https://doi.org/10.1007/s10910-014-0386-1

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