Semi-Classical Behavior of the Spectral Function

2005/02/26 by Ivana Alexandrova, Alexandrova, Ivana
Mathematics · #35P05 #35S99 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35P05 #msc:35S99

paper · pdf · doi:10.48550/arxiv.math/0502555

10 pages

arxiv created 2005/02/26 · arxiv updated 2009/12/01

Abstract

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spectral function.

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