For one dimensional Schrödinger operators, in terms of local behavior of the potential, we give some comparison theorems for their eigenvalues. As an application, some monotone properties of the first eigenvalue of stepfunction potentials are given.
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Chie-Ping Chu, Some Comparison Theorems on Eigenvalues for One Dimensional Schrödinger Operators with Applications. Z. Anal. Anwend. 29 (2010), no. 1, pp. 117–124DOI 10.4171/ZAA/1401