4 papers · 1 filter
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 $…
Classical Density Functional Theory: The Local Density Approximation
Michal Jex, Mathieu Lewin, Peter Madsen
We prove that the lowest free energy of a classical interacting system at temperature with a prescribed density profile can be approximated by the local free energy $\in…
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…
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…