A comment on the common one-dimensional derivation of the van der Waals forces

In many physical text-books a simple one-dimensional model is used to derive the characteristic 1/R ⁷-dependence of the attractive van der Waals forces. We show that this calculation is wrong. The long range forces in this simple model are not attractive but repulsive proportional to 1/R ⁶. Only a three-dimensional calculation yields the correct behavior.