  We show that the RST model describing the exactly soluble black hole model
can have a dynamical wormhole solution along with an appropriate boundary
condition. The necessary exotic matter which is usually negative energy density
is remarkably produced by the quantization of the infalling matter fields. Then
the asymptotic geometry in the past is two-dimensional anti-de Sitter(AdS$_2$),
which implies the exotic matter is negative. As time goes on, the wormhole
eventually evolves into the black hole and its Hawking radiation appears. The
throat of the static RST wormhole is lower-bounded but in the presence of
infalling matter it collapses to a black hole.
