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

Abstract

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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.

Keywords

• 1D Schrödinger operator
• magnetic potential
• zero-energy resonance
• half-bound state
• short range interaction
• point interaction