We prove sharp lower bounds on the spectral gap of 1-dimensional Schrodinger 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 Horvath 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.

中文翻译：

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具有单井势的一维 Robin Schrödinger 算子的光谱间隙

对于 Robin 参数的每个值，我们证明了具有 Robin 边界条件的一维薛定谔算子的光谱间隙的尖锐下界。特别是，我们的下限适用于具有居中过渡点的单井电位。这一结果扩展了 Cheng 等人的工作。和 Horvath 在 Neumann 和 Dirichlet 端点案例中的插值机制。我们还建立在 Andrews、Clutterbuck 和 Hauer 最近在凸和对称单井势的情况下的工作。特别是，我们表明光谱间隙是对称势的 Robin 参数的增函数。