Geometric Spectral Inversion
Mathematical Physics
2012-06-20 v1 math.MP
Abstract
A discrete eigenvalue E_n of a Schroedinger operator H = -\Delta + vf(r) is given, as a function F_n(v) of the coupling parameter v\ge v_c. It is shown how the potential shape f(x) can be reconstructed from F_n(v). A constructive inversion algorithm and a functional inversion sequence are both discussed.
Cite
@article{arxiv.1206.4288,
title = {Geometric Spectral Inversion},
author = {Richard L. Hall},
journal= {arXiv preprint arXiv:1206.4288},
year = {2012}
}
Comments
20 pages, 7 figures; 13th Regional Conference on Mathematical Physics, October 27 - 31, 2010, Antalya, Turkey