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Scaling limits in the 3-D Schrödinger-Poisson system

✍ Scribed by J.L. López; J. Soler

Book ID
104349960
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
306 KB
Volume
10
Category
Article
ISSN
0893-9659

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✦ Synopsis

The equivalence between the Schr'ddinger formalism for pure quantum states and the Wigner representation of quantum mechanics, and the importance of the latter in semiconductor modelling motivates the analysis of the large-time behaviour for the SchrSdinger-Poisson problem arising in this context. Using an appropriate rescaling group and some self-similarity properties of the rescaled solutions, it is proved that the kinetic energy effects in the rescaled system vanish for large times. Then, when the time goes to infinity, the limit potential of the original system can be identified as a Coulomb potential.

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