Semiclassical spectral invariants for Schrodinger operators
Author(s)
Guillemin, Victor W.; Wang, Zuoqin
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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.
Description
Original manuscript September 23, 2009
Date issued
2012-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of Differential Geometry
Publisher
International Press of Boston, Inc.
Citation
Guillemin, Victor, and Wang, Zuoqin. "Semiclassical Invariants for Schrodinger Operators." Journal of Differential Geometry 91.1 (2012): 103-128.
Version: Original manuscript
ISSN
0022-040X
1945-743X