Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. I. Asymptotic Expansion Formulas

2008 ◽  
Vol 131 (5) ◽  
pp. 867-916 ◽  
Author(s):  
A. Astrauskas
Keyword(s):  
Asymptotic Expansion ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Extremal Theory

Asymptotic expansion of the scattering matrix associated with matrix Schrödinger operator

2012 ◽  
Vol 80 (1-2) ◽  
pp. 57-78 ◽  
Author(s):  
Hamadi Baklouti ◽  
Slaheddine Ben Abdeljeilil
Keyword(s):  
Asymptotic Expansion ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Schrodinger Operator

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.

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