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arXiv · 1710.01403

Unique Continuation for the Magnetic Schr\"odinger Equation

Andre Laestadius·Michael Benedicks·Markus Penz
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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.

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Andre Laestadius, Michael Benedicks, Markus Penz. 2017-10-03. Unique Continuation for the Magnetic Schr\"odinger Equation. https://doi.org/10.1002/qua.26149

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