Coulomb states in nanostructures, accidental degeneracy, and the Laplace–Runge–Lenz operator

The energy-level structure of spatially indirect Coulomb complexes is investigated. Two limiting cases that correspond to the two-dimensional hydrogen atom and planar isotropic harmonic oscillator are characterized by accidental degeneracy are considered. Numerical calculations are used to trace the evolution of the energy-level structure between these two limiting cases.