Simultaneous degeneracy of the confined 2D hydrogen atom energy levels

Using the Numerov-Cooley numerical method, we report several interesting characteristics of the eigenspectrum of 2D hydrogen atom confined inside an impenetrable circular boundary of radius rho(c). At the confinement radius, rho(c), exactly equal to the location of the only radial node of the unconfined atom state (l + 2, l), the successive pairs of the confined atom states (nl) and (n + 1, l + 2), where n >= l + 2, are found to become degenerate. Accurate calculations of static dipole polarizability are reported for several confining radii using the standard second-order perturbation theory.