Absence of eigenvalues of two-dimensional magnetic Schroedinger operators

TL;DR

This paper develops a multiplier method to identify conditions under which two-dimensional magnetic Schrödinger operators have no eigenvalues, including cases with complex potentials and Aharonov-Bohm magnetic fields.

Contribution

It introduces a new multiplier technique to prove the absence of eigenvalues for a broad class of magnetic Schrödinger operators, extending to complex and singular potentials.

Findings

Established sufficient conditions for no eigenvalues in magnetic Schrödinger operators.

Extended results to complex-valued electric potentials.

Covered singular magnetic potentials like Aharonov-Bohm fields.

Abstract

By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point spectrum. The settings of complex-valued electric potentials and singular magnetic potentials of Aharonov-Bohm field are also covered.