A discussion is presented of the quantum-mechanical derivation of the Boltzmann equation, along with a demonstration that use of the superlattice representation of McIrvine and Overhauser enables avoidance of singular and non-physical terms in the Hamiltonian of the neutron-moderator system. The formal validity of the Boltzmann equation in finite systems is analyzed, and it is shown that the transport description is physically meaningful for systems of dimensions >>10−4 cm.