Unique Continuation for the Magnetic Schr\"odinger Equation
Mathematical Physics
2024-10-22 v4 math.MP
Quantum Physics
Abstract
The unique-continuation property from sets of positive measure is here proven for the many-body magnetic Schr\"odinger equation. This property guarantees that if a solution of the Schr\"odinger 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
Cite
@article{arxiv.1710.01403,
title = {Unique Continuation for the Magnetic Schr\"odinger Equation},
author = {Andre Laestadius and Michael Benedicks and Markus Penz},
journal= {arXiv preprint arXiv:1710.01403},
year = {2024}
}