  The existence of anomalous symmetry-breaking solutions of the SO(2,1)
commutator algebra is explicitly extended beyond the case of scale-invariant
contact interactions. In particular, the failure of the conservation laws of
the dilation and special conformal charges is displayed for the two-dimensional
inverse square potential. As a consequence, this anomaly appears to be a
generic feature of conformal quantum mechanics and not merely an artifact of
contact interactions. Moreover, a renormalization procedure traces the
emergence of this conformal anomaly to the ultraviolet sector of the theory,
within which lies the apparent singularity.
