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arXiv · 1811.07213

Some remarks on 1D Schrödinger operators with localized magnetic and electric potentials

Yuriy Golovaty
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Abstract

One-dimensional Schrödinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized $δ$-like magnetic fields are combined with $δ\,'$-like perturbations of the electric potentials as well as localized rank-two perturbations. The limit results obtained heavily depend on zero-energy resonances of the electric potentials. In particular, the approximation for a wide class of point interactions in one dimension is obtained.

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Yuriy Golovaty. 2018-11-17. Some remarks on 1D Schrödinger operators with localized magnetic and electric potentials. https://doi.org/10.3389/fphy.2019.00070

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