MCS-MP Seminar: Severin Schraven

Speaker: Severin Schraven (TU Munich)

Title: Two-sided Lieb-Thirring Bounds

Abstract: We discuss upper and lower bounds for the number of eigenvalues of semi-bounded Schrödinger operators in all spatial dimensions. For atomic Hamiltonians with Kato potentials one can strengthen the result to obtain two-sided estimates for the sum of the negative eigenvalues. Instead of being in terms of the potential itself, as in the usual Lieb-Thirring result, the bounds
are in terms of the landscape function, also known as the torsion function, which is a solution of $(−\Delta + V +M)u_M = 1$ in ${\mathbb R}^d$; here $M \in {\mathbb R}$ is chosen so that the operator is positive.

This talk is based on the preprint arXiv:2403.19023 which is joint work with S. Bachmann and R. Froese.