Semiclassical spectral invariants for Schrodinger operators
Name
Guillemin_Semiclassical spectral.pdf
Size
284.68 KB
Format
Adobe PDF
Checksum (MD5)
f9fc052b2e867908199cd866c59c2166
Author(s)
Guillemin, Victor W.
Wang, Zuoqin
Date Issued
May 2012
Journal
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
Abstract
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
http://projecteuclid.org/euclid.jdg/1343133702
