On-diagonal singularities of the Green functions for Schroedinger operators

Details On-diagonal singularities of the Green functions for Schroedinger operators On-diagonal singularities of the Green functions for Schroedinger operators

2004-11-26

arxiv.org/abs/math-ph/0411078v2

J.Math.Phys. 46 (2005) 113508

Physics

Mathematical Physics

17 pages

Scientific paper

10.1063/1.2113087

We investigate the behavior of the Green functions of Schroedinger operators near the diagonal. The only non-trivial cases, where the on-diagonal singularities are non-zero 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 non-regular potentials. Some examples illustrating dependence of the singularity on general scalar and gauge potentials are presented.

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