Schroedinger Operator with Strong Magnetic Field near Boundary

2010/05/03 by Victor Ivrii, Ivrii, Victor
Computer Science · Mathematics · #35P20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1005.0244

openalex publication_date 2010/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider 2-dimensional Schroedinger operator with the non-degenerating magnetic field in the domain with the boundary and under certain non-degeneracy assumptions we derive spectral asymptotics with the remainder estimate better than O(h^-1), up to O(μ^-1h^-1) and the principal part \asymp h^-2 where h≪ 1 is Planck constant and μ≫ 1 is the intensity of the magnetic field; μh ≤ 1. We also consider generalized Schrödinger-Pauli operator in the same framework albeit with μh≥ 1 and derive spectral asymptotics with the remainder estimate up to O(1) and with the principal part \asymp μh^-1, or, under certain special circumstances with the principal part \asymp μ^1/2 h^-1/2.

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