  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.
