  This is the first in a series of papers addressing the phenomenon of
dimensional transmutation in nonrelativistic quantum mechanics within the
framework of dimensional regularization. Scale-invariant potentials are
identified and their general properties are derived. A strategy for dimensional
renormalization of these systems in the strong-coupling regime is presented,
and the emergence of an energy scale is shown, both for the bound-state and
scattering sectors. Finally, dimensional transmutation is explicitly
illustrated for the two-dimensional delta-function potential.
