  Certain time dependent configurations in the c=1 matrix model correspond to
string theory backgrounds which have spacelike boundaries and appear
geodesically incomplete. We investigate quantum mechanical properties of a
class of such configurations in the matrix model, in terms of fermionic
eigenvalues. We describe Hamiltonian evolution of the eigenvalue density using
several different time variables, some of which are infinite and some of which
are finite in extent. We derive unitary transformations relating these
different descriptions, and use those to calculate fermion correlators in the
time dependent background. Using the chiral formalism, we write the time
dependent configurations as a state in the original matrix model Hilbert space.
