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 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.