Spectra of Schrödinger Operators on Equilateral Quantum Graphs
Spectra of Schrödinger Operators on Equilateral Quantum Graphs
复制标题
等边量子图上薛定谔算子的谱
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Konstantin Pankrashkin
中科院分区：
文献类型：
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作者：
Konstantin Pankrashkin
We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, it is shown that the spectrum on the quantum graph is the preimage of the combinatorial spectrum under a certain entire function. Using this Correspondence we show that the number of gaps in the spectrum of the Schrödinger operators admits an estimate from below in terms of the Hill operator independently of the graph structure.
