Recovering the shape of a quantum caterpillar tree by two spectra
Mathematical Physics
2023-03-30 v2 math.MP
Abstract
We show how to find the shape of an equilateral caterpillar tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm-Liouville equation on this tree. We prove that in the case of a caterpillar tree the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree.
Keywords
Cite
@article{arxiv.2303.14670,
title = {Recovering the shape of a quantum caterpillar tree by two spectra},
author = {Dmytro Kaliuzhnyi-Verbovetskyi and Vyacheslav Pivovarchik},
journal= {arXiv preprint arXiv:2303.14670},
year = {2023}
}
Comments
9 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2301.05939