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We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a $d$-dimensional cylinder. The potential $V$ is assumed to be periodic with respect to some lattice. We establish the absolu...
We say that a discrete set $X =\{x_n\}_{n\in\dN_0}$ on the half-line $$0=x_0 < x_1 infty$$ is sparse in the case the distances $\Delta x_n = x_{n+1} -x_n$ between neighboring p...
We prove that for any fixed trigonometric polynomial potential satisfying a genericity condition, the spectrum of the two dimension periodic Schr¨odinger operator has finite multiplicity and the Fouri...
Lower Bounds for the Infimum of the Spectrum of the Schrödinger Operator in $\mathbb{R}^n$ and the Sobolev Inequalities.
2005Vol.44No.2pp.252-254DOI: “Eigen-Operator”Method of the Square of Schrödinger Operator in Interaction Picture and Its Application in Describing Parametric Amplifiers FAN...
2004Vol.42No.6pp.824-826DOI: Determining Energy Eigenvalues of Dynamic Systems by Finding `Eigen-operator' of Square of Schrödinger Operator FAN Hong-Yi,1,2 XU Xue-Fen,3 an...
In this paper, we consider the Schrödinger operators defined by the differential expression Lu= - D u + q(x)u in d-dimensional paralellepiped F, with the Dirichlet and the Neumann boundary condit...

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