  We study quantum mechanically the self-similar black hole formation by
collapsing scalar field and find the wave functions that give the correct
semiclassical limit. In contrast to classical theory, the wave functions for
the black hole formation even in the supercritical case have not only incoming
flux but also outgoing flux. From this result we compute the rate for the black
hole formation. In the subcritical case our result agrees with the
semiclassical tunneling rate. Furthermore, we show how to recover the classical
evolution of black hole formation from the wave function by defining the
Hamilton-Jacobi characteristic function as $W = \hbar {\rm Im} \ln \psi$. We
find that the quantum corrected apparent horizon deviates from the classical
value only slightly without any qualitative change even in the critical case.
