  Levi-Civita spacetimes have classical naked singularities. They also have
quantum singularities. Quantum singularities in general relativistic spacetimes
are determined by the behavior of quantum test particles. A static spacetime is
said to be quantum mechanically singular if the spatial portion of the wave
operator is not essentially self-adjoint on a $C_{0}^{\infty}$ domain in
$L^{2}$, a Hilbert space of square integrable functions. Here we summarize how
Weyl's limit point-limit circle criterion can be used to determine whether a
wave operator is essentially self-adjoint and how this test can then be applied
to scalar wave packets in Levi-Civita spacetimes with and without a
cosmological constant to help elucidate the physical properties of these
spacetimes.
