论文标题
带有单孔电势的干扰性schrödinger操作员的Lieb-Thirring类型边界
Lieb-Thirring type bounds for perturbed Schrödinger operators with single-well potentials
论文作者
论文摘要
我们证明了在扰动的Schrödinger操作员$ H_0-V $和$ H_0 $的最低特征值之间的特征值之间的距离之和。我们的结果适用于操作员$ h_0 =-Δ-v_0 $在一个维度上具有单孔电势。我们依靠众所周知的换向方法的变体。在Pöschl-Teller和Coulomb案例中，我们能够使用明确的分解来建立改进的界限。
We prove an upper bound on the sum of the distances between the eigenvalues of a perturbed Schrödinger operator $H_0-V$ and the lowest eigenvalue of $H_0$. Our results hold for operators $H_0=-Δ-V_0$ in one dimension with single-well potentials. We rely on a variation of the well-known commutation method. In the Pöschl-Teller and Coulomb cases we are able to use the explicit factorisations to establish improved bounds.
