Volume 26, 2020
|Number of page(s)||18|
|Published online||08 September 2020|
Numerical reconstruction of the first band(s) in an inverse Hill’s problem
Ecole des Ponts ParisTech,
2 Ecole des Ponts ParisTech & INRIA, Champs-sur-Marne, France.
3 CEREMADE, Paris-Dauphine University, PSL University, 75016 Paris, France.
* Corresponding author: email@example.com
Accepted: 26 April 2019
This paper concerns an inverse band structure problem for one dimensional periodic Schrödinger 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).
Mathematics Subject Classification: 35P05 / 58C40 / 34K29 / 34L15
Key words: Inverse spectral theory / Hill’s operator / periodic Schrödinger operator / band structure / optimisation
© EDP Sciences, SMAI 2020
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