  The quantum mechanical analysis of the canonical hamiltonian description of
the effective action of a SDp-brane in bosonic ten dimensional Type II
supergravity in a homogeneous background is given. We find exact solutions for
the corresponding quantum theory by solving the Wheeler-deWitt equation in the
late-time limit of the rolling tachyon. The probability densities for several
values of p are shown and their possible interpretation is discussed. In the
process the effects of electromagnetic fields are also incorporated and it is
shown that in this case the interpretation of tachyon regarded as ``matter
clock'' is modified.
