  The dynamics of a thin spherically symmetric shell of zero-rest-mass matter
in its own gravitational field is studied. A form of action principle is used
that enables the reformulation of the dynamics as motion on a fixed background
manifold. A self-adjoint extension of the Hamiltonian is obtained via the group
quantization method. Operators of position and of direction of motion are
constructed. The shell is shown to avoid the singularity, to bounce and to
re-expand to that asymptotic region from which it contracted; the dynamics is,
therefore, truly unitary. If a wave packet is sufficiently narrow and/or
energetic then an essential part of it can be concentrated under its
Schwarzschild radius near the bounce point but no black hole forms. The quantum
Schwarzschild horizon is a linear combination of a black and white hole
apparent horizons rather than an event horizon.
