Sharp Spectral Asymptotics for four-dimensional Schroedinger operator with a strong magnetic field. II

2006/12/10 by Ivrii, Victor
#35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0612252

Abstract

I consider 4-dimensional Schrödinger operator with the generic non-degenerating magnetic field and for a generic potential I derive spectral asymptotics with the remainder estimate O(μ^-1h^-3) and the principal part \asymp h^-4 where h≪ 1 is Planck constant and μ≫ 1 is the intensity of the magnetic field. For general potentials remainder estimate O(μ^-1h^-3+μ²h^-2) is achieved.

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