Counterexamples to the Landis conjecture in dimensions three and higher

Rupert L. Frank; Paata Ivanisvili

Counterexamples to the Landis conjecture in dimensions three and higher

Analysis of PDEs 2026-08-01 v1 Mathematical Physics

Authors: Rupert L. Frank , Paata Ivanisvili

Abstract

In every dimension three and higher we construct a nonzero function that satisfies the stationary Schr\"odinger equation with bounded, real-valued potential and decays like $\exp(-c|x|^{4/3})$ . This gives a counterexample to the Landis conjecture in dimension three and higher.

Keywords

Landis conjecture stationary Schrödinger equation counterexample decay rate bounded potential

Cite

@article{arxiv.2608.00802,
  title  = {Counterexamples to the Landis conjecture in dimensions three and higher},
  author = {Rupert L. Frank and Paata Ivanisvili},
  journal= {arXiv preprint arXiv:2608.00802},
  year   = {2026}
}

Comments

34 pages