Unique Continuation for the Magnetic Schrödinger Equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866914979135881216 |
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| author | Laestadius, Andre Benedicks, Michael Penz, Markus |
| author_facet | Laestadius, Andre Benedicks, Michael Penz, Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_01403 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Unique Continuation for the Magnetic Schrödinger Equation Laestadius, Andre Benedicks, Michael Penz, Markus Mathematical Physics Quantum Physics 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. |
| title | Unique Continuation for the Magnetic Schrödinger Equation |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/1710.01403 |