Open Access
May 2012 Semiclassical Spectral Invariants for Schrödinger Operators
Victor Guillemin, Zuoqin Wang
J. Differential Geom. 91(1): 103-128 (May 2012). DOI: 10.4310/jdg/1343133702


In this article we show how to compute the semiclassical spectral measure associated with the Schrödinger operator on $\mathbb{R}^n$, 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 Schrödinger operator on $\mathbb{R}^2$ 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 Schrödinger operator with its Birkhoff canonical form.


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Victor Guillemin. Zuoqin Wang. "Semiclassical Spectral Invariants for Schrödinger Operators." J. Differential Geom. 91 (1) 103 - 128, May 2012.


Published: May 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1273.35198
MathSciNet: MR2944963
Digital Object Identifier: 10.4310/jdg/1343133702

Rights: Copyright © 2012 Lehigh University

Vol.91 • No. 1 • May 2012
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