Schr{\'o}dinger eigenfunctions sharing the same modulus and applications to the control of quantum systems

Autor:	Boscain, Ugo, Balc'H, Kévin Le, Sigalotti, Mario
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	In this paper we investigate when linearly independent eigenfunctions of the Schr\''odinger operator may have the same modulus. General properties are established and the one-dimensional case is treated in full generality. The study is motivated by its application to the bilinear control of the Schr{\"o}dinger equation. By assuming that the potentials of interaction satisfy a saturation property and by adapting a strategy recently proposed by Duca and Nersesyan, we discuss when the system can be steered arbitrarily fast between energy levels. Extensions of the previous results to quantum graphs are finally presented.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.08341 Zobrazit plný text záznamu View this record from Arxiv