Semiclassical spectral invariants for Schrodinger operators
Original manuscript September 23, 2009
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
International Press of Boston, Inc.
2013
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| Online Access: | http://hdl.handle.net/1721.1/80279 https://orcid.org/0000-0003-2641-1097 |
| _version_ | 1826195256907923456 |
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| author | Guillemin, Victor W. Wang, Zuoqin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor W. Wang, Zuoqin |
| author_sort | Guillemin, Victor W. |
| collection | MIT |
| description | Original manuscript September 23, 2009 |
| first_indexed | 2024-09-23T10:09:50Z |
| format | Article |
| id | mit-1721.1/80279 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:09:50Z |
| publishDate | 2013 |
| publisher | International Press of Boston, Inc. |
| record_format | dspace |
| spelling | mit-1721.1/802792022-09-26T16:07:50Z Semiclassical spectral invariants for Schrodinger operators Guillemin, Victor W. Wang, Zuoqin Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor W. Original manuscript September 23, 2009 In this article we show how to compute the semiclassical spectral measure associated with the Schrodinger operator on R[superscript n], and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schrodinger operator on R[superscript 2] with a radially symmetric electric potential, V, and magnetic potential, B, both V and B are spectrally determined.) We also show that in one dimension there is a very simple explicit identity relating the spectral measure of the Schrodinger operator with its Birkhoff canonical form. National Science Foundation (U.S.) (Grant DMS-1005696) 2013-08-26T19:37:07Z 2013-08-26T19:37:07Z 2012-05 2010-02 Article http://purl.org/eprint/type/JournalArticle 0022-040X 1945-743X http://hdl.handle.net/1721.1/80279 Guillemin, Victor, and Wang, Zuoqin. "Semiclassical Invariants for Schrodinger Operators." Journal of Differential Geometry 91.1 (2012): 103-128. https://orcid.org/0000-0003-2641-1097 en_US http://projecteuclid.org/euclid.jdg/1343133702 Journal of Differential Geometry Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf International Press of Boston, Inc. arXiv |
| spellingShingle | Guillemin, Victor W. Wang, Zuoqin Semiclassical spectral invariants for Schrodinger operators |
| title | Semiclassical spectral invariants for Schrodinger operators |
| title_full | Semiclassical spectral invariants for Schrodinger operators |
| title_fullStr | Semiclassical spectral invariants for Schrodinger operators |
| title_full_unstemmed | Semiclassical spectral invariants for Schrodinger operators |
| title_short | Semiclassical spectral invariants for Schrodinger operators |
| title_sort | semiclassical spectral invariants for schrodinger operators |
| url | http://hdl.handle.net/1721.1/80279 https://orcid.org/0000-0003-2641-1097 |
| work_keys_str_mv | AT guilleminvictorw semiclassicalspectralinvariantsforschrodingeroperators AT wangzuoqin semiclassicalspectralinvariantsforschrodingeroperators |