scholarly journals Quaternionic factorization of the Schrödinger operator and its applications to some first-order systems of mathematical physics

2003 ◽  
Vol 36 (44) ◽  
pp. 11285-11297 ◽  
Author(s):  
Viktor G Kravchenko ◽  
Vladislav V Kravchenko
Keyword(s):  
Schrödinger Operator ◽  
Mathematical Physics ◽  
Schrodinger Operator ◽  
First Order

Inverse scattering for the higher order Schrödinger operator with a first order perturbation

2019 ◽  
Vol 27 (3) ◽  
pp. 409-427
Author(s):  
Hua Huang ◽  
Zhiwen Duan ◽  
Quan Zheng
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operator ◽  
Scattering Matrix ◽  
Higher Order ◽  
Zero Order ◽  
Schrodinger Operator ◽  
Scattering Problems ◽  
First Order ◽  
Fixed Energy ◽  
First Order Perturbation

Abstract This paper concerns inverse scattering problems at a fixed energy for the higher order Schrödinger operator with the first order perturbed potentials in dimensions {n\geq 3} . We show that the scattering matrix uniquely determines the first order perturbed potentials and the zero order potentials.

A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE

2000 ◽  
Vol 12 (12) ◽  
pp. 1655-1667 ◽  
Author(s):  
C. ALLARD ◽  
R. FROESE
Keyword(s):  
Schrödinger Operator ◽  
Binary Tree ◽  
Invariant Subspaces ◽  
Schrodinger Operator ◽  
Conjugate Operator ◽  
Order Difference ◽  
First Order ◽  
Decay Condition ◽  
Mourre Estimate

Let G be a binary tree with vertices V and H be a Schrödinger operator acting on ℓ2 (V). A decomposition of the space ℓ2 (V) into invariant subspaces is exhibited yielding a conjugate operator A for use in the Mourre estimate. We show that for potentials q satisfying a first order difference decay condition, a Mourre estimate for H holds.

scholarly journals Structure of the Spectra and Resonances of Schrödinger Operators

2020 ◽  
Vol 12 (1) ◽  
pp. 83-102
Author(s):  
Tahar Bouguetaia ◽  
Bekkai Messirdi
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Schrödinger Operator ◽  
Periodic Potential ◽  
Schrödinger Operators ◽  
Mathematical Physics ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Operator Spectrum

The main goal of this paper is to study the spectrum and resonances of several classes of Schrödinger operators. Two important examples occurring in mathematical physics are discussed: harmonic oscillator and Hamiltonian of hydrogen atom. Keywords: Schrödinger operator, Spectrum, Periodic potential, Resonances.

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
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