The geometry of Fermi varieties plays critical roles in studying many topics of periodic
Schrödinger operators. In this article, we will first discuss the irreducibility of the Fermi variety …

In this paper, we consider the Schrödinger equation, Hu=-u^"+\left (V\left (x\right)+ V_0\left
(x\right)\right) u= Eu, H u=− u ″+(V (x)+ V 0 (x)) u= E u, where V 0 (x) is 1-periodic and V (x) …

One Dimensional Discrete Schrödinger Operators with Resonant Embedded Eigenvalues |
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In this paper, we consider Schr\" odinger operators on $ L^ 2 (0,\infty) $ given by\begin
{align} Hu=(H_0+ V) u=-u^{\prime\prime}+ V_0u+ Vu= Eu,\nonumber\end {align} where …

For perturbed Stark operators H u=− u′′− xu+ qu, the author has proved that lim sup x→∞
x 1 2| q (x)| must be larger than 1 2 N 1 2 in order to create N linearly independent …

We consider the Dirac equation on $ L^ 2 (\mathbb {R})\oplus L^ 2 (\mathbb {R}) $\begin
{align} Ly=\begin {pmatrix} 0&-1 1&0\end {pmatrix}\begin {pmatrix} y_1 y_2\end …

Sergey Naboko authored a large amount of papers on the spectral theory of Jacobi
operators. The main themes of his work are the existence of eigenvalues embedded into the …