scholarly journals A Weyl–Titchmarsh type formula for a discrete Schrödinger operator with Wigner–von Neumann potential

2010 ◽  
Vol 201 (2) ◽  
pp. 167-189 ◽  
Author(s):  
Jan Janas ◽  
Sergey Simonov
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Von Neumann ◽  
Type Formula

scholarly journals Weyl—Titchmarsh-type formula for periodic Schrödinger operator with Wigner—von Neumann potential

2013 ◽  
Vol 143 (2) ◽  
pp. 401-425 ◽  
Author(s):  
Pavel Kurasov ◽  
Sergey Simonov
Keyword(s):  
Continuous Spectrum ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
Von Neumann ◽  
Type Formula ◽  
Generalized Eigenvectors ◽  
Neumann Type ◽  
Periodic Schrödinger Operator

The Schrödinger operator on the half-line with periodic background potential perturbed by a certain potential of Wigner—von Neumann type is considered. The asymptotics of generalized eigenvectors for λ ϵ ℂ+ and on the absolutely continuous spectrum is established. The Weyl—Titchmarsh-type formula for this operator is proven.

ON THE SPECTRAL AND SCATTERING THEORY OF THE SCHRÖDINGER OPERATOR WITH SURFACE POTENTIAL

2000 ◽  
Vol 12 (04) ◽  
pp. 561-573 ◽  
Author(s):  
AYHAM CHAHROUR ◽  
JAOUAD SAHBANI
Keyword(s):  
Continuous Spectrum ◽  
Surface Potential ◽  
Schrödinger Operator ◽  
Scattering Theory ◽  
Schrodinger Operator ◽  
Absolutely Continuous Spectrum ◽  
Discrete Schrödinger Operator ◽  
Absolutely Continuous ◽  
Spectral And Scattering Theory

We consider a discrete Schrödinger operator H=-Δ+V acting in ℓ2 (ℤd+1), with potential V supported by the subspace ℤd×{0}. We prove that σ (-Δ)=[-2 (d+1), 2(d+1)] is contained in the absolutely continuous spectrum of H. For this we develop a scattering theory for H. We emphasize the fact that this result applies to arbitrary potentials, so it depends on the structure of the problem rather than on a particular choice of the potential.

Sign in / Sign up

Export Citation Format

Share Document