On-diagonal singularities of the Green functions for Schrödinger operators

2004/11/30 by Jochen Bruening, Jochen Brüning, V. A. Geyler +2 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP

paper · pdf · doi:10.1063/1.2113087

published as J.Math.Phys. 46 (2005) 113508 · 17 pages

arxiv created 2005/05/26 · openalex publication_date 2005/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the behavior of the Green functions of Schrödinger operators near the diagonal. The only nontrivial cases, where the on-diagonal singularities are nonzero and do not depend on the spectral parameter, are two and three dimensions. In the case of two dimensions we show that the singularity is independent of both the scalar and the gauge potentials. In dimension three, we obtain conditions for preserving the singularity under perturbations by nonregular potentials. Some examples illustrating dependence of the singularity on general scalar and gauge potentials are presented.

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