Level crossings of eigenvalues of the Schrödinger Hamiltonian of the isotropic harmonic oscillator perturbed by a central point interaction in different dimensions

In this brief presentation, some striking differences between level crossings of eigenvalues in one dimension (harmonic or conic oscillator with a central nonlocal $\delta'$-interaction) or three dimensions (isotropic harmonic oscillator with a three-dimensional delta located at the origin) and those occurring in the two-dimensional analogue of these models will be highlighted.