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2020 Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum
Mouez Dimassi
Tunisian J. Math. 2(1): 197-215 (2020). DOI: 10.2140/tunis.2020.2.197

Abstract

In the semiclassical regime (i.e., ϵ0), we study the effect of a slowly varying potential V(ϵt,ϵz) on the magnetic Schrödinger operator P=Dx2+(Dz+μx)2 on a strip [a,a]×z. The potential V(t,z) is assumed to be smooth. We derive the semiclassical dynamics and we describe the asymptotic structure of the spectrum and the resonances of the operator P+V(ϵt,ϵz) for ϵ small enough. All our results depend on the eigenvalues corresponding to Dx2+(μx+k)2 on L2([a,a]) with Dirichlet boundary condition.

Citation

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Mouez Dimassi. "Semiclassical approximation of the magnetic Schrödinger operator on a strip: dynamics and spectrum." Tunisian J. Math. 2 (1) 197 - 215, 2020. https://doi.org/10.2140/tunis.2020.2.197

Information

Received: 10 October 2018; Revised: 17 November 2018; Accepted: 2 December 2018; Published: 2020
First available in Project Euclid: 2 April 2019

zbMATH: 07074074
MathSciNet: MR3933395
Digital Object Identifier: 10.2140/tunis.2020.2.197

Subjects:
Primary: 35P20, 47A55, 47N50, 81Q10, 81Q15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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