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

• Main Author: Yuriy Golovaty
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2019-05-01
• Series: Frontiers in Physics
• Subjects: 1D Schrödinger operator; magnetic potential; zero-energy resonance; half-bound state; short range interaction; point interaction
• Online Access: https://www.frontiersin.org/article/10.3389/fphy.2019.00070/full
• ISSN: 2296-424X

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.