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Research in Group: Jex, Hundertmark & Lange
Meeting coordinated by Michal Jex with the presence of Dirk Hundertmark and Markus Lange.
Stay from April 17th to 28th, 2026
Existence of eigenvalues and the asymptotic behaviour of the corresponding eigenfunctions are important properties of quantum systems. The recently accepted paper (Quantum systems at the brink: helium-type systems, accepted to ARMA) provides a new method how to address these problems without a need for a safety distance to the essential spectrum unlike previously used methods. We plan to apply this method to an atom with N electrons.
We intend to optimize the results from our preprint on sharp exponential decay rates for atomic eigenfunctions in the subcritical case, where all ionization energies are positive. We use custom localization techniques and energy bounds which are necessary to prove optimal decay estimates. The main difficulty comes from finding suitable localization regions which allows for sharp asymptotic, because it was already established that conical regions are insufficient. In addition, we will work on the critical case when the first ionization energies are zero.
Stay from April 17th to 28th, 2026
Existence of eigenvalues and the asymptotic behaviour of the corresponding eigenfunctions are important properties of quantum systems. The recently accepted paper (Quantum systems at the brink: helium-type systems, accepted to ARMA) provides a new method how to address these problems without a need for a safety distance to the essential spectrum unlike previously used methods. We plan to apply this method to an atom with N electrons.
We intend to optimize the results from our preprint on sharp exponential decay rates for atomic eigenfunctions in the subcritical case, where all ionization energies are positive. We use custom localization techniques and energy bounds which are necessary to prove optimal decay estimates. The main difficulty comes from finding suitable localization regions which allows for sharp asymptotic, because it was already established that conical regions are insufficient. In addition, we will work on the critical case when the first ionization energies are zero.