  We study the analytic structure of the S-matrix which is obtained from the
reduced Wheeler-DeWitt wave function describing spherically symmetric
gravitational collapse of massless scalar fields. The complex simple poles in
the S-matrix lead to the wave functions that satisfy the same boundary
condition as quasi-normal modes of a black hole, and correspond to the bounded
states of the Euclidean Wheeler-DeWitt equation. These wave function are
interpreted as quantum instantons.
