标题： 一维强魏尔定律的简短证明 显示英文标题

标题： A short proof of a strong Weyl law in dimension 1

摘要： 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. 此近似值的误差在$1/n$阶以内，因此使得结果严格强于这些算子负特征值数量的经典Weyl定律。 显示英文摘要

摘要： 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.