3 papers
math-ph2026
Eigenstates with Infinite Position Moments
Michal Jex
We prove necessary and sufficient conditions for the Schrödinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $…
math-ph2020
Quantum Systems at The Brink: Properties of Atomic Bound States at The Ionization Threshold
Dirk Hundertmark, Michal Jex, Markus Lange
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the…
math-ph2019
Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; Atoms
Dirk Hundertmark, Michal Jex, Markus Lange
It is well known that -electron atoms undergoes unbinding for a critical charge of the nucleus , i.e. the atom has eigenstates for the case and it has no bound sta…