Semi-classical limit of Schrodinger-Poisson equations in space dimension at least 3

Details Semi-classical limit of Schrodinger-Poisson equations in space dimension at least 3 Semi-classical limit of Schrodinger-Poisson equations in space dimension at least 3

2006-10-05

arxiv.org/abs/math/0610182v1

J. Differential Equations 233 (2007) 241-275

Mathematics

Analysis of PDEs

30 pages. To appear in JDE

Scientific paper

10.1016/j.jde.2006.10.003

We prove the existence of solutions to the Schrodinger-Poisson system on a time interval independent of the Planck constant, when the doping profile does not necessarily decrease at infinity, in the presence of a subquadratic external potential. The lack of integrability of the doping profile is resolved by working in Zhidkov spaces, in space dimension at least three. We infer that the main quadratic quantities (position density and modified momentum density) converge strongly as the Planck constant goes to zero. When the doping profile is integrable, we prove pointwise convergence.

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