  We discuss the quantization of a spherical dust shell in a rigorous manner.
Classically, the shell can collapse to form a black hole with a singularity. In
the quantum theory, we construct a well-defined self-adjoint extension for the
Hamilton operator. As a result, the evolution is unitary and the singularity is
avoided. If we represent the shell initially by a narrow wave packet, it will
first contract until it reaches the region where classically a black hole would
form, but then re-expands to infinity. In a way, the state can be interpreted
as a superposition of a black hole with a white hole.
