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Journal Article

Unique continuation for the magnetic Schrödinger equation


Penz,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Laestadius, A., Benedicks, M., & Penz, M. (2020). Unique continuation for the magnetic Schrödinger equation. International Journal of Quantum Chemistry, 120(8): e26149. doi:10.1002/qua.26149.

Cite as: https://hdl.handle.net/21.11116/0000-0005-F2CC-4
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.