  It is well known that a system, S, weakly coupled to a heat bath, B, is
described by the canonical ensemble when the composite, S+B, is described by
the microcanonical ensemble corresponding to a suitable energy shell. This is
true both for classical distributions on the phase space and for quantum
density matrices. Here we show that a much stronger statement holds for quantum
systems. Even if the state of the composite corresponds to a single wave
function rather than a mixture, the reduced density matrix of the system is
canonical, for the overwhelming majority of wave functions in the subspace
corresponding to the energy interval encompassed by the microcanonical
ensemble. This clarifies, expands and justifies remarks made by Schr\"odinger
in 1952.
