The variable-phase approach is applied to scattering and bound states in an attractive
Coulomb potential, statically screened by a two-dimensional (2D) electron gas. A 2D
formulation of Levinson's theorem is used for bound-state counting and a hitherto
undiscovered, simple relationship between the screening length and the number of bound
states is found. As the screening length is increased, sets of bound states with differing
quantum numbers appear degenerately.