English

The van der Waals interaction in one, two and three dimensions

Quantum Physics 2015-01-22 v2 Mesoscale and Nanoscale Physics

Abstract

The van der Waals interaction between two polarizable atoms is considered. In three dimensions the standard form with an attractive 1/R61/|R|^6 potential is obtained from second-order quantum perturbation theory. When the electron motion is restricted to lower dimensions (but the 1/R1/|R| Coulomb potential is retained), new terms in the expansion appear and alter both the sign and the R|R| dependence of the interaction.

Keywords

Cite

@article{arxiv.1401.8141,
  title  = {The van der Waals interaction in one, two and three dimensions},
  author = {A. C. Ipsen and K. Splittorff},
  journal= {arXiv preprint arXiv:1401.8141},
  year   = {2015}
}

Comments

15 pages, 3 figures. Intended for educational purposes. V2: References and appendix added, figures edited. Version to appear in AJP

R2 v1 2026-06-22T02:58:31.381Z