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.

mathematical physicsspectral theory

Audience: researchers in the topic

Munich-Copenhagen-Santiago Mathematical Physics seminar

Series comments: The MAS-MP seminar series has now changed name to MCS-MP.

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