Semi-Classical Behavior of the Spectral Function

Details Semi-Classical Behavior of the Spectral Function Semi-Classical Behavior of the Spectral Function

2005-02-26

arxiv.org/abs/math/0502555v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

We study the semi-classical behavior of the spectral function of the Schr\"{o}dinger 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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