AUTHOR=Golovaty Yuriy 

TITLE=Some Remarks on 1D Schrödinger Operators With Localized Magnetic and Electric Potentials

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00070

DOI=10.3389/fphy.2019.00070

ISSN=2296-424X

ABSTRACT=<p>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 <italic>δ</italic>-like magnetic fields are combined with <italic>δ′</italic>-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.</p>