Premium
The two‐dimensional Wigner–Poisson problem for an electron gas in the charge neutral case
Author(s) -
Arnold Anton,
Nier Francis
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140902
Subject(s) - mathematics , poisson distribution , poisson's equation , charge (physics) , electron , schrödinger's cat , mathematical physics , mathematical analysis , quantum mechanics , physics , statistics
We prove the global existence of a unique classical solution of the two‐dimensional Wigner–Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.