  We present a full treatment of the microcanonical ensemble of the ideal
hadron-resonance gas in a quantum-mechanical framework which is appropriate for
the statistical model of hadronization. By using a suitable transition operator
for hadronization we are able to recover the results of the statistical theory,
particularly the expressions of the rates of different channels. Explicit
formulae are obtained for the phase space volume or density of states of the
ideal relativistic gas in quantum statistics which, for large volumes, turn to
a cluster decomposition whose terms beyond the leading one account for
Bose-Einstein and Fermi-Dirac correlations. The problem of the computation of
the microcanonical ensemble and its comparison with the canonical one, which
will be the main subject of a forthcoming paper, is addressed.
