Klein paradox and Scattering theory for the semi-classical Dirac equation

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dc.creatorKhochman, Abdallah
dc.date2007-11-20
dc.date.accessioned2026-07-07T08:44:01Z
dc.date.available2026-07-07T08:44:01Z
dc.descriptionWe study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming and outgoing plane wave solutions is established. The corresponding scattering matrix is unitary. We obtain an asymptotic expansion, with respect to the semi-classical parameter $h$, of the scattering matrix in the cases of the Klein paradox, the total transmission and the total reflection. Finally, we treat the scattering problem in the zero mass case.
dc.description25 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0711.3155
dc.identifierhttp://arxiv.org/abs/0711.3155
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142514
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject81Q05, 47A40, 34L40, 34E20, 34M60
dc.titleKlein paradox and Scattering theory for the semi-classical Dirac equation
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