Absence of eigenvalues of Dirac and Pauli Hamiltonians via the method of multipliers

TL;DR

This paper develops a multiplier method to identify conditions on electromagnetic fields that ensure Dirac, Pauli, and Schrödinger operators have no eigenvalues, advancing spectral analysis in quantum mechanics.

Contribution

It introduces a new multiplier approach to establish eigenvalue absence for Dirac, Pauli, and Schrödinger operators under specific electromagnetic conditions.

Findings

Eigenvalues are absent under certain magnetic and electric potentials.

The method applies to Schrödinger, Pauli, and Dirac operators.

Results extend to operators with supersymmetric structures.

Abstract

By developing the method of multipliers, we establish sufficient conditions on the magnetic field and the complex, matrix-valued electric potential, which guarantee that the corresponding system of Schr\"odinger operators has no point spectrum. In particular, this allows us to prove analogous results for Pauli operators under the same electromagnetic conditions and, in turn, as a consequence of the supersymmetric structure, also for magnetic Dirac operators.