The two-dimensional Wigner–Poisson problem for an electron gas in the charge neutral case

✍ Scribed by Anton Arnold; Francis Nier

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 700 KB
• Volume: 14
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670140902

✦ Synopsis

Abstract

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.