Abstract
We consider the Schrödinger operator on two types of domains depending on a small parameter ε: dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a “limit” operator defined on the limit domain.
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Ciuperca, I.S. Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness. Journal of Dynamics and Differential Equations 10, 73–108 (1998). https://doi.org/10.1023/A:1022640429041
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DOI: https://doi.org/10.1023/A:1022640429041