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Symmetry preserving self-adjoint extensions of Schrödinger operators with singular potentials
Symmetry preserving self-adjoint extensions Schrö dinger operators singular potentials
2011/1/21
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Prob-lems of this type naturally arise when considering two- and ...
Rescaled Mourre's commutator theory, application to Schrödinger operators with oscillating potential
Mourre’s commutator theory Mourre estimate limiting absorption principle
2011/1/18
We present a variant of Mourre’s commutator theory. We apply it to prove the limiting absorption principle for Schr¨odinger operators with a perturbedWigner-Von Neumann potential at suitable energies....
On the finiteness of the Morse Index for Schrödinger operators
the Morse Index Schrö dinger operators
2010/11/19
Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the exist...
Spectral statistics for random Schrödinger operators in the localized regime
Spectral statistics random Schrö dinger operators the localized regime
2010/11/15
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy $E$ in the localized phase. Assume ...
We systematically describe and classify 1-dimensional Schr¨odinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new ...
A variational approach to dislocation problems for periodic Schrödinger operators
Schr¨odinger operators eigenvalues spectral gaps
2010/12/8
As a simple model for lattice defects like grain boundaries in solid state physics we consider potentials which are obtained from a periodic potential V = V (x, y) on R2 with period lattice Z2 by sett...
Defect Modes and Homogenization of Periodic Schrödinger Operators
Defect Modes Homogenization of Periodic Schrö dinger Operators
2010/11/30
Defect Modes and Homogenization of Periodic Schrödinger Operators.
On the spectrum of skew-shift Schrödinger operators
spectrum ergodic Schrodinger operators skew-shift
2010/11/30
I prove that the spectrum of a skew-shift Schrodinger operator contains larges interval in the semi-classical regime. In the semi-classical limit,these intervals approach the range of the potential.
Comparison of Green Functions for Generalized Schrödinger Operators on $C^{1,1}$-Domains
Green function Schrö dinger operator $3G$-Theorem
2008/7/1
Comparison of Green Functions for Generalized Schrödinger Operators on $C^{1,1}$-Domains.