Note on the Retarded van der Waals Potential within the Dipole Approximation
Mathematical Physics
2020-04-28 v3 math.MP
Abstract
We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei together with the Coulomb interaction between the electrons can be approximated by harmonic potentials. By an exact diagonalization method, we prove that the binding energy of the two hydrogen atoms behaves as , provided that the distance between atoms is sufficiently large. We employ the Feynman's representation of the quantized radiation fields which enables us to diagonalize Hamiltonians, rigorously. Our result supports the famous conjecture by Casimir and Polder.
Cite
@article{arxiv.1902.05207,
title = {Note on the Retarded van der Waals Potential within the Dipole Approximation},
author = {Tadahiro Miyao},
journal= {arXiv preprint arXiv:1902.05207},
year = {2020}
}