  We study, in general terms, the process by which a pure state can
``self-thermalize'' and {\em appear} to be described by a microcanonical
density matrix. This requires a quantum mechanical version of the Gibbsian
coarse graining that conceptually underlies classical statistical mechanics. We
introduce some extra degrees of freedom that are necessary for this.
Interaction between these degrees and the system can be understood as a process
of resonant absorption and emission of ``soft quanta''. This intuitive picture
allows one to state a criterion for when self thermalization occurs. This
paradigm also provides a method for calculating the thermalization rate using
the usual formalism of atomic physics for calculating decay rates. We contrast
our prescription for coarse graining, which is somewhat dynamical, with the
earlier approaches that are intrinsically kinematical. An important motivation
for this study is the black hole information paradox.
