1-D Schrödinger Operators with Local Interactions on a Discrete Set with Unbounded Potential
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- 作者：Aleksandra Yu. Ananieva
- 关键词：Schrödinger operator ; unbounded potential ; self ; adjoint ; local point interaction ; discreteness
- 刊名：Journal of Mathematical Sciences
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：220
- 期：5
- 页码：554-583
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer US
- ISSN：1573-8795
- 卷排序：220
文摘
We study spectral properties of the one-dimensional Schrödinger operators \( {\mathrm{H}}_{\mathrm{X},\alpha, \mathrm{q}}:=-\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}+\mathrm{q}(x)+{\varSigma_x}_{{}_n}\in X{\alpha}_n\delta \left(x-{x}_n\right) \) with local interactions, d* = 0, and an unbounded potential q being a piecewise constant function, by using the technique of boundary triplets and the corresponding Weyl functions. Under various sufficient conditions for the self-adjointness and discreteness of Jacobi matrices, we obtain the condition of self-adjointness and discreteness for the operator HX,α,q.