  We study a broad class of spacetimes whose metric coefficients reduce to
powers of a radius r in the limit of small r. Among these four-parameter
"power-law" metrics we identify those parameters for which the spacetimes have
classical singularities as r approaches 0. We show that a large set of such
classically singular spacetimes is nevertheless nonsingular quantum
mechanically, in that the Hamiltonian operator is essentially self-adjoint, so
that the evolution of quantum wave packets lacks the ambiguity associated with
scattering off singularities. Using these metrics, the broadest class yet
studied to compare classical with quantum singularities, we explore the
physical reasons why some that are singular classically are "healed" quantum
mechanically, while others are not. We show that most (but not all) of the
remaining quantum-mechanically singular spacetimes can be excluded if either
the weak energy condition or the dominant energy condition is invoked, and we
briefly discuss the effect of this work on the strong cosmic censorship
hypothesis.
