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Von Neumann-Wigner theorem: Level repulsion and degenerate eigenvalues

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Abstract

We investigate the spectral properties of Schrödinger operators with point interactions, focusing attention on the interplay between level repulsion (von Neumann-Wigner theorem) and the symmetry of the confi.guration of point interactions. The explicit solution of the problem allows observing level repulsion for two centers. For a large number of centers, we investigate the families of point interactions leading to the maximum degeneracy.

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Authors and Affiliations

  1. Physics Research Institute, St. Petersburg University, St. Petersburg, Russia

    Yu. N. Demkov & P. B. Kurasov

  2. Department of Mathematics, Lund University, Lund, Sweden

    Yu. N. Demkov & P. B. Kurasov

Authors
  1. Yu. N. Demkov
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  2. P. B. Kurasov
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Corresponding author

Correspondence to P. B. Kurasov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 68–85, October, 2007.

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Demkov, Y.N., Kurasov, P.B. Von Neumann-Wigner theorem: Level repulsion and degenerate eigenvalues. Theor Math Phys 153, 1407–1422 (2007). https://doi.org/10.1007/s11232-007-0124-y

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  • DOI: https://doi.org/10.1007/s11232-007-0124-y

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