量子图谱的特征值对磁扰的稳定性和特征函数的节点计数。
Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions.
机构信息
Department of Mathematics, Texas A&M University, , College Station, TX 77843-3368, USA.
出版信息
Philos Trans A Math Phys Eng Sci. 2013 Dec 16;372(2007):20120522. doi: 10.1098/rsta.2012.0522. Print 2014 Jan 28.
We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros of the nth eigenfunction of the Schrödinger operator on a quantum graph is related to the stability of the nth eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the nth eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to φ - (n-1).
我们证明了量子图上薛定谔算子的第 n 个本征函数的零点个数与磁场位势对算子的微扰的第 n 个特征值的稳定性之间的一个类似的磁结点定理：更确切地说，我们将第 n 个特征值视为磁场微扰的函数，并证明其在零磁场下的 Morse 指标等于 φ - (n-1)。
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