Simultaneous degeneracy of the confined 2D hydrogen atom energy levels

Abstract

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 ρ_c. At the confinement radius, ρ_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.