QLunch: Michal Jex

Speaker: Michal Jex

Title: Quantum Systems at the Brink: Properties of Bounds States Approaching the Continuum

Abstract: Understanding how isolated bound states interact with the continuous spectrum is an important problem in quantum mechanics. In this talk, we present recent results on eigenstates of Schrödinger operator which approach the continuum. We derive necessary and sufficient conditions for the existence of threshold eigenstates and analyze how the asymptotic properties of these states change as they approach the continuum. We illustrate the theoretical rasults through concrete examples.

Jex M.: Eigenstates with Infinite Position Moments, accepted into Reviews in Mathematical Physics, arXiv: 2605.06504 (2026)

Hundertmark D., Jex M., Lange M.: Quantum Systems at The Brink: Helium-type systems, preprint arXiv: 1908.04883, accepted into ARMA (2026)

Hundertmark, D., Jex, M., Lange, M.: Quantum Systems at The Brink, in Quantum Mathematics I, Springer INdAM series (2023)

Hundertmark D., Jex M., Lange M.: Quantum Systems at The Brink-Existence and Decay Rates of Bound States at Thresholds; Critical Potentials and dimensionality, Forum of Mathematics, Sigma, 11, E61 (2023)