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Some remarks on 1D Schrödinger operators with localized magnetic and electric potentials (1811.07213v1)
Published 17 Nov 2018 in math.SP, math-ph, and math.MP
Abstract: One-dimensional Schr\"odinger 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 $\delta$-like magnetic fields are combined with $\delta\,'$-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.