论文标题
具有单孔电势的1-DRobinSchrödinger操作员的光谱间隙
Spectral gaps of 1-D Robin Schrödinger operators with single-well potentials
论文作者
论文摘要
我们证明，对于罗宾参数的每个值，具有罗宾边界条件的1维schrödinger算子的光谱间隙上的尖锐下限。特别是，我们的下限适用于具有中心过渡点的单孔电势。该结果扩展了Cheng等人的工作。在诺伊曼（Neumann）和迪利奇（Dirichlet）端点案件中，霍尔瓦斯（Horváth）进行了插值制度。在凸和对称的单孔电势的情况下，我们还基于安德鲁斯，克鲁特巴克和豪尔的最新工作。特别是，我们表明光谱差距是对称势的罗宾参数的增加功能。
We prove sharp lower bounds on the spectral gap of 1-dimensional Schrödinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lower bounds apply to single-well potentials with a centered transition point. This result extends work of Cheng et al. and Horváth in the Neumann and Dirichlet endpoint cases to the interpolating regime. We also build on recent work by Andrews, Clutterbuck, and Hauer in the case of convex and symmetric single-well potentials. In particular, we show the spectral gap is an increasing function of the Robin parameter for symmetric potentials.
