Numerical reconstruction of the first band(s) in an inverse Hill's problem
Optimization and Control
2017-09-22 v1
Abstract
This paper concerns an inverse band structure problem for one dimensional periodic Schr\"odinger operators (Hill's operators). Our goal is to find a potential for the Hill's operator in order to reproduce as best as possible some given target bands, which may not be realisable. We recast the problem as an optimisation problem, and prove that this problem is well-posed when considering singular potentials (Borel measures). We then propose different algorithms to tackle the problem numerically.
Keywords
Cite
@article{arxiv.1709.07023,
title = {Numerical reconstruction of the first band(s) in an inverse Hill's problem},
author = {Athmane Bakhta and Virginie Ehrlacher and David Gontier},
journal= {arXiv preprint arXiv:1709.07023},
year = {2017}
}