Given a Schrödinger operator with a real-valued potential on a bounded, convex domain or a bounded interval we prove inequalities between the eigenvalues corresponding to Neumann and Dirichlet boundary conditions, respectively. The obtained inequalities depend partially on monotonicity and convexity properties of the potential. The results are counterparts of classical inequalities for the Laplacian but display some distinction between the one-dimensional case and higher dimensions.

中文翻译：

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薛定谔算子的 Neumann 和 Dirichlet 特征值之间的不等式

给定在有界凸域或有界区间上具有实值势的薛定谔算子，我们分别证明对应于 Neumann 和 Dirichlet 边界条件的特征值之间的不等式。获得的不等式部分取决于势能的单调性和凸性。结果是拉普拉斯算子的经典不等式的对应物，但在一维情况和更高维度之间显示出一些区别。