Dirk Hundertmark: Quantum systems at The Brink: Sharp bounds. The asymptotic behavior of bound states.

Speaker
Dirk Hundertmark, Karlsruhe Institute of Technology

Abstract
Since 1982 Agmon’s method is the tool to systematically study the asymptotic behavior of bound states in quantum mechanics. It is based on the concept of what is now known as “Agmon metric” and has numerous applications to many body quantum mechanics. As beautiful as it is, Agmon’s method has two shortfalls: It needs an epsilon loss in the highest order coefficients to control error terms and it needs a safety distance of the eigenvalue to the edge of the essential spectrum. The epsilon loss somewhat weakens the results and the safety distance prevents the method to be applied in critical situations, where the eigenvalue is at the edge of the essential spectrum. We show that this common belief, the necessity of an epsilon loss and a safety distance to the essential spectrum, is not set in stone. This requires some new ideas, however 😉 Joint work with Michal Jex and Markus Lange.