A short proof of a strong Weyl law in dimension 1

Abstract: We will consider the Dirichlet realization of a Schrödinger operator on a bounded interval and with a continuous potential, and discuss a slightly non-standard formulation of the associated Weyl law. Instead of studying only the number of negative eigenvalues, we ask: When exactly does the eigenvalue counting function change its value? For a particular class of potentials we provide an asymptotic answer to this question which is *not* a consequence of the usual Weyl law (while the usual Weyl law for the number of negative eigenvalues does follow from our result). If time allows, we will suggest how we at this point in time believe similar results in more general setups would have to look. Based on arxiv.org/abs/2403.05137.

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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