The spectral shift function and Levinson's theorem for quantum star graphs
Spectral Theory
2015-06-05 v1 Mathematical Physics
math.MP
Abstract
We consider the Schr\"odinger operator on a star shaped graph with edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula.
Cite
@article{arxiv.1205.1772,
title = {The spectral shift function and Levinson's theorem for quantum star graphs},
author = {Semra Demirel},
journal= {arXiv preprint arXiv:1205.1772},
year = {2015}
}