Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal mehtod (when the problem admits an image solution). We then illustrate this method in a couple of simple but important cases, including the atom-sphere system. Particularly, in our last example, we present an original result, namely, the van der Waals force between an atom and a boss hat made of a grounded conducting material.

We obtain analytically the exact nonretarded dispersive interaction energy between an atom and a perfectly conducting disk. We consider the atom in the symmetry axis of the disk and assume that the atom is predominantly polarizable in the direction of this axis. For this situation we discuss the finite-size effects on the corresponding interaction energy. We follow the recent procedure introduced by Eberlein and Zietal together with the old and powerful Sommerfeld's image method for nontrivial geometries. For the sake of clarity we present a detailed discussion of Sommerfeld's image method. Comparing our results for the atom-disk system with those recently obtained for an atom near a conducting plane with a circular aperture, we discuss the nonadditivity of the van der Waals interactions involving an atom and two complementary surfaces. We show that there is a given ratio z/a between the distance z from the atom to the center of the disk (aperture) and the radius of the disk a (aperture) for which nonadditivity effects vanish. Qualitative arguments suggest that this quite unexpected result will occur not only for a circular hole, but for any other symmetric hole.

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 semiinfinite 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.