  Using a Hamiltonian formulation of the spherically symmetric gravity-scalar
field theory adapted to flat spatial slicing, we give a construction of the
reduced Hamiltonian operator. This Hamiltonian, together with the null
expansion operators presented in an earlier work, form a framework for studying
gravitational collapse in quantum gravity. We describe a setting for its
numerical implementation, and discuss some conceptual issues associated with
quantum dynamics in a partial gauge fixing.
