Derivation of Schrödinger Poisson as the Non-relativistic Limit of Klein-Gordon Maxwell

Philippe Bechouche (), Norbert J. Mauser () and Sigmund Selberg ()
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Philippe Bechouche: Univ. Wien, Wolfgang Pauli Inst. c/o Inst. f. Math.
Norbert J. Mauser: Univ. Wien, Wolfgang Pauli Inst. c/o Inst. f. Math.
Sigmund Selberg: Univ. Wien, Wolfgang Pauli Inst. c/o Inst. f. Math.

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 357-367 from Springer

Abstract: Abstract We deal with the derivation of the Schrödinger-Poisson system as a non-relativistic limit (i.e. c → − where c is the speed of light) of the Klein-Gordon-Maxwell or the Dirac-Maxwell system on ℝ1+3 We deal with convergence in the energy space C([0, T]; H 1). We use and motivate a splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to electrons and positrons. The crucial technique is to use the Klainerman-Machedon machinery for the appropriately scaled system which has null form structure for the case of Coulomb gauge.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_32

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DOI: 10.1007/978-3-642-55711-8_32

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