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Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder
spectrum the periodic Schrö dinger operator layer smooth cylinder
2010/11/11
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...
Singular continuous spectrum of one-dimensional Schrödinger operator with point interactions on a sparse set
Singular continuous spectrum one-dimensional Schrö dinger operator
2010/11/18
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...
Eigenfunction localization for the 2D periodic Schrödinger operator
Eigenfunction localization 2D periodic Schrö dinger operator
2010/11/30
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
Optimal lower bound Infimum spectrum Schrö dinger operator Sobolev inequality
2008/7/1
Lower Bounds for the Infimum of the Spectrum of the Schrödinger Operator in $\mathbb{R}^n$ and the Sobolev Inequalities.
On $L^p$-Estimates for the Time Dependent Schrödinger Operator on $L^2$
Schrö dinger Equation Strichartz Estimates and Self-adjointness
2008/6/30
On $L^p$-Estimates for the Time Dependent Schrödinger Operator on $L^2$.
Asymptotic Formulas for the Resonance Eigenvalues of the Schrödinger Operator
Asymptotic Formulas Schrö dinger Operator Resonance Eigenvalues
2010/2/26
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...