The high-order nonrelativistic Hamiltonian of electromagnetic system
Abstract
The nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas-Kroll-Hess approach. Their relativistic Hamiltonians are expanded on the potential, and the Hamiltonians containing one- and two-photon potentials are derived. The nonrelativistic Hamiltonians up to order are obtained by applying Taylor expansion on momentum, and the result of spin-1/2 spinor is coincided with the result obtained by applying scattering matching approach in the Ref.~[Phys. Rev. A {\bf 100}, 012513 (2019)]. Then, the singularities in Hamiltonian of Coulomb systems are separated out and cancelled. The regularized Hamiltonian up to order for scaler and electron in Coulomb field are obtained. The numerical results of relativistic corrections are coincided with the relativistic theory. The regularized Hamiltonian up to for multi-electrons in Coulomb field are also derived.
Keywords
Cite
@article{arxiv.2003.10068,
title = {The high-order nonrelativistic Hamiltonian of electromagnetic system},
author = {Wanping Zhou and Xuesong Mei and Haoxue Qiao},
journal= {arXiv preprint arXiv:2003.10068},
year = {2022}
}