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Unique continuation for the magnetic Schrödinger equation
Author(s) -
Laestadius Andre,
Benedicks Michael,
Penz Markus
Publication year - 2020
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26149
Subject(s) - continuation , property (philosophy) , measure (data warehouse) , schrödinger equation , quantum , quantum mechanics , physics , mathematics , schrödinger's cat , mathematical physics , statistical physics , theoretical physics , classical mechanics , computer science , philosophy , programming language , epistemology , database
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.