1205.1772 (Semra Demirel)

The spectral shift function and Levinson's theorem for quantum star
graphs    [PDF]

Semra Demirel

We consider the Schr\"odinger operator on a star shaped graph with $n$ 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.

View original: http://arxiv.org/abs/1205.1772