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.
Keywords: Hohenberg‐Kohn theorem; Kato class; magnetic Schrödinger equation; molecular Hamiltonian; unique‐continuation property.
© 2020 The Authors. International Journal of Quantum Chemistry published by Wiley Periodicals, Inc.