On Wave Operators for the Multidimensional Electromagnetic Schrödinger Operator in the Divergent Form

2017 ◽  
Vol 68 (8) ◽  
pp. 1153-1164
Author(s):  
A. R. Aliev ◽  
É. Kh. Éivazov
Keyword(s):  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Divergent Form ◽  
Wave Operators

Schrödinger operator with decreasing potential in a cylinder

2021 ◽  
Vol 33 (1) ◽  
pp. 155-178
Author(s):  
N. Filonov
Keyword(s):  
Continuous Spectrum ◽  
Bounded Domain ◽  
Invariance Principle ◽  
Schrödinger Operator ◽  
Singular Continuous Spectrum ◽  
Schrodinger Operator ◽  
Limiting Absorption Principle ◽  
Content Type ◽  
Wave Operators ◽  
The Absolute

The Schrödinger operator − Δ + V ( x , y ) -\Delta + V(x,y) is considered in a cylinder R m × U \mathbb {R}^m \times U , where U U is a bounded domain in R d \mathbb {R}^d . The spectrum of such an operator is studied under the assumption that the potential decreases in longitudinal variables, | V ( x , y ) | ≤ C ⟨ x ⟩ − ρ |V(x,y)| \le C \langle x\rangle ^{-\rho } . If ρ > 1 \rho > 1 , then the wave operators exist and are complete; the Birman invariance principle and the limiting absorption principle hold true; the absolute continuous spectrum fills the semiaxis; the singular continuous spectrum is empty; the eigenvalues can accumulate to the thresholds only.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
Sign in / Sign up

Export Citation Format

Share Document