Eur. Phys. J. D 7, 1-4 (1999)
https://doi.org/10.1007/s100530050339

Phases of wave functions and level repulsion

Centre for Nonlinear Studies and Department of Physics, University of the Witwatersrand, PO Wits 2050, Johannesburg South Africa

Received: 7 January 1999
Revised: 15 March 1999
Published online: 15 August 1999

Abstract

Avoided level crossings are associated with exceptional points which are the singularities of the spectrum and eigenfunctions, when considered as functions of a complex coupling parameter. It is shown that the wave function of one state changes sign but not the other, if the exceptional point is encircled in the complex plane. An experimental setup is suggested where this peculiar phase change could be observed.