Asymptotics of the eigenvalues of a discrete Schrödinger operator with zero-range potential

2012 ◽  
Vol 76 (5) ◽  
pp. 946-966
Author(s):  
Saidakhmat N Lakaev ◽  
Shohruh Yu Holmatov
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Range Potential ◽  
Zero Range ◽  
Asymptotics Of The Eigenvalues

scholarly journals The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum

2021 ◽  
Vol 2070 (1) ◽  
pp. 012017
Author(s):  
J.I. Abdullaev ◽  
A.M. Khalkhuzhaev
Keyword(s):  
Essential Spectrum ◽  
Schrödinger Operator ◽  
Three Dimensional ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
Dimensional Lattice ◽  
Pairwise Potential ◽  
Zero Range

Abstract We consider a three-particle discrete Schrödinger operator Hμγ (K), K 2 T3 associated to a system of three particles (two fermions and one different particle) interacting through zero range pairwise potential μ > 0 on the three-dimensional lattice Z 3. It is proved that the operator Hμγ (K), ||K|| < δ, for γ > γ0 has at least two eigenvalues in the gap of the essential spectrum for sufficiently large μ > 0.

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