The existence and location of eigenvalues of the one-particle discrete Schrodinger operator on a lattice

2020 ◽  
Vol 2020 (2) ◽  
pp. 119-133
Author(s):  
S.N. Lakaev ◽  
I.U. Alladustova
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Discrete Schrödinger Operator ◽  
The One

scholarly journals On the spectral properties of the Schrödinger operator with a periodic PT-symmetric potential

2017 ◽  
Vol 14 (05) ◽  
pp. 1750065 ◽  
Author(s):  
Oktay Veliev
Keyword(s):  
Schrödinger Operator ◽  
Spectral Properties ◽  
Schrodinger Operator ◽  
Symmetric Potential ◽  
One Dimensional ◽  
Symmetric Complex ◽  
The One ◽  
Complex Valued

In this paper, we investigate the spectrum and spectrality of the one-dimensional Schrödinger operator with a periodic PT-symmetric complex-valued potential.

The one-dimensional Schrödinger operator with point δ- and δ-interactions

2008 ◽  
Vol 84 (1-2) ◽  
pp. 125-129 ◽  
Author(s):  
N. I. Goloshchapova ◽  
L. L. Oridoroga
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
One Dimensional ◽  
The One

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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