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

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 $\delta$-like magnetic fields are combined with $\delta {}^{\prime }$-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.

13 pages. arXiv admin note: text overlap with arXiv:1206.1941

References in corpus (1)

• Two-parametric ${\delta }^{\prime }$-interactions: approximation by Schrödinger operators with localized rank-two perturbations

Cited by in corpus (2)

• Band spectra of periodic hybrid $\delta$-${\delta }^{\prime }$ structures
• On negative eigenvalues of 1D Schrödinger operators with ${\delta }^{\prime }$-like potentials