Unique continuation for the magnetic Schrödinger equation.

The unique-continuation property from sets of positive measure is here proven for the many-body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger equation vanishes on a set of positive measure, then it is identically zero. We explicitly consider potentials written as sums of either one-body or two-body functions, typical for Hamiltonians in many-body quantum mechanics. As a special case, we are able to treat atomic and molecular Hamiltonians. The unique-continuation property plays an important role in density-functional theories, which underpins its relevance in quantum chemistry.