Asymptotic Behavior to the 3-d Schrödinger/hartree Poisson and Wigner Poisson Systems
نویسندگان
چکیده
Using an appropriate scaling group for the 3-D Schrödinger–Poisson equation and the equivalence between the Schrödinger formalism and the Wigner representation of quantum mechanics it is proved that, when time goes to infinity, the limit of the rescaled self-consistent potential can be identified as the Coulomb potential. As a consequence, Schrödinger–Poisson and Wigner–Poisson systems are asymptotically simplified and their long-time behavior is explained through the solutions of the corresponding linear limit problems.
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