  Derivation of the canonical (or Boltzmann) distribution based only on quantum
dynamics is discussed. Consider a closed system which consists of mutually
interacting subsystem and heat bath, and assume that the whole system is
initially in a pure state (which can be far from equilibrium) with small energy
fluctuation. Under the "hypothesis of equal weights for eigenstates", we derive
the canonical distribution in the sense that, at sufficiently large and typical
time, the (instantaneous) quantum mechanical expectation value of an arbitrary
operator of the subsystem is almost equal to the desired canonical expectation
value. We present a class of examples in which the above derivation can be
rigorously established without any unproven hypotheses.
