Von Neumann-Wigner theorem: Level repulsion and degenerate eigenvalues

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.