On the eigenfunctions of no-pair operators in classical magnetic fields - Mathematical Physics

On the eigenfunctions of no-pair operators in classical magnetic fields - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider a relativistic no-pair model of a hydrogenic atom in a classical,exterior magnetic field. First, we prove that the corresponding Hamiltonian issemi-bounded below, for all coupling constants less than or equal to thecritical one known for the Brown-Ravenhall model, i.e., for vanishing magneticfields. We give conditions ensuring that its essential spectrum equals1,\infty and that there exist infinitely many eigenvalues below 1. The restenergy of the electron is 1 in our units. Assuming that the magnetic vectorpotential is smooth and that all its partial derivatives increasesubexponentially, we finally show that an eigenfunction corresponding to aneigenvalue \lambda<1 is smooth away from the nucleus and that its partialderivatives of any order decay pointwise exponentially with any ratea<1-\lambda^2^{1-2}, for \lambda\in0,1, and a<1, for \lambda<0.

Author: Oliver Matte, Edgardo Stockmeyer

Source: https://arxiv.org/