Geodesic
Von Neumann--Wigner theorem: Level repulsion and degenerate eigenvalues
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 68-85

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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 configuration 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.
Keywords: von Neumann–Wigner theorem, zero-range potential, extension theory, inverse spectral problem. 
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     author = {Yu. N. Demkov and P. B. Kurasov},
     title = {Von {Neumann--Wigner} theorem: {Level} repulsion and degenerate eigenvalues},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {68--85},
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     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a5/}
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Yu. N. Demkov; P. B. Kurasov. Von Neumann--Wigner theorem: Level repulsion and degenerate eigenvalues. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 68-85. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a5/