Recovering the shape of a quantum tree by scattering data
Mathematical Physics
2023-03-14 v2 math.MP
Abstract
We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of a equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree. We assume that the potential on the lead is zero identically and the potentials on the finite edges are L_2-functions. We show how to find the shape of the tree using the S-function of the scattering problem.
Keywords
Cite
@article{arxiv.2303.02440,
title = {Recovering the shape of a quantum tree by scattering data},
author = {Vyacheslav Pivovarchik},
journal= {arXiv preprint arXiv:2303.02440},
year = {2023}
}
Comments
15 pages, 3 figures. arXiv admin note: text overlap with arXiv:2301.05939