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arXiv · 2403.05137

A short proof of a strong Weyl law in dimension 1

August Bjerg
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Abstract

For the Dirichlet realization of $-d^2/dx^2-\lambda^2V$ on a bounded interval, with $V$ a positive $C^2$ potential bounded away from $0$ and $\lambda>0$ a large parameter, we prove an asymptotic law for the values $\lambda_n$ of $\lambda$ at the $n^{\text{th}}$ appearance of a new negative eigenvalue. This approximation is correct up to an error of order $1/n$, thus making the result strictly stronger than the classical Weyl law for the number of negative eigenvalues for these operators.

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August Bjerg. 2024-03-08. A short proof of a strong Weyl law in dimension 1. https://arxiv.org/abs/2403.05137

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