  We analyse the effective potential of the scalar wave equation near generic
space-time singularities of power-law type (Szekeres-Iyer metrics) and show
that the effective potential exhibits a universal and scale invariant leading
x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that
the metrics satisfy the strict Dominant Energy Condition (DEC). This result
parallels that obtained in hep-th/0403252 for probes consisting of families of
massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The
detailed properties of the scalar wave operator depend sensitively on the
numerical coefficient of the x^{-2}-term, and as one application we show that
timelike singularities satisfying the DEC are quantum mechanically singular in
the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We
also comment on some related issues like the near-singularity behaviour of the
scalar fields permitted by the Friedrichs extension.
