Scattering amplitude for the Schr odinger equation with strong magnetic eld

Michel Laurent

Description

& $ % Scattering amplitude for the Schr?odinger equation with strong magnetic eld Forges-les-eaux, June 6-10, 2005 Laurent Michel 1

• reed-simon


• magnetic eld


• unique ?2 ?


• avron-herbst-simon


• scattering matrix


• schrodinger equation


• schrodinger operator

Sujets

• Michel
• S-matrix
• Schrödinger equation

Informations

• Publié par: pefav
• Nombre de lectures: 8
• Langue: English

Extrait

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ScatteringamplitudefortheSchr ¨ odinger equation with strong magnetic field

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Forges-les-eaux,June6-10,

Laurent Michel

1

2005

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I.1 Framework

I Introduction

We consider the Schro¨  dinger operator with constant magnetic field



H(b) = H 0 (b) +b V(x, y, z)

where  H (b) = ∂ b  2 ∂   b 2 x  2  
z . 0 x∂ i 2 +y+ y∂ i Herex∈R,y∈R,z∈R n   2 ,b >0is a parameter and ∈[0,1]is fixed. In all this talk, we will assume thatVsatisfies the following hypothesis Assumption 1 V(x, y, z) =V ∞ (z) +W(x, y, z) withV ∞ ∈C 0 ∞ (R n   2 ),W∈C 0 ∞ (R n )andV, V ∞ 0.

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2

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