Sommerfeld's image method in the calculation of van der Waals forces

TL;DR

This paper combines Sommerfeld's image method with a recent approach to calculate van der Waals forces between an atom and conducting surfaces of arbitrary shape, extending previous techniques to more complex geometries.

Contribution

It introduces a novel combination of classical and modern methods to evaluate dispersive interactions for arbitrary geometries, including semi-infinite planes.

Findings

Successfully applied to atom-plane interactions

Extended to arbitrary-shaped conducting surfaces

Provides a framework for future complex geometries

Abstract

We show how the image method can be used together with a recent method developed by C. Eberlein and R. Zietal to obtain the dispersive van der Waals interaction between an atom and a perfectly conducting surface of arbitrary shape. We discuss in detail the case of an atom and a semi- infinite conducting plane. In order to employ the above procedure to this problem it is necessary to use the ingenious image method introduced by Sommerfeld more than one century ago, which is a generalization of the standard procedure. Finally, we briefly discuss other interesting situations that can also be treated by the joint use of Sommerfeld's image technique and Eberlein-Zietal method.