# Homework Help: Van Der-Waals forces.

1. Dec 11, 2009

### MathematicalPhysicist

1. The problem statement, all variables and given/known data
The van der waals forces describe the forces between neutral atoms, separated by a distance much larger than the typical size of a single atom, as we saw in class.
Therefore we describe the interaction between the atoms by: $$W=W_{dd}+W_{dq}+W_{qd}+W_{qq}+...$$ i.e W is the energy sum which has contributions from dipole-dipole, quadrapule-dipole, quadrapule-quadrapule and so.
In class we were shown that the first order correction due to dipole dipole interaction $$W_{dd}$$ vanishes, and we solved this with second order perturbation theory.
But this is actually justified if first order correction of all other contriubtions to W vanish as well. Show that this is the case here.

2. Relevant equations

3. The attempt at a solution
I know that I need to find the quadrapule tensor Q for two atoms, but not sure how does this look like? i.e I know the general equation for the potential of a quadrapule and the euqation for the quadrapule itself, but don't know how to write Q explictly.
P.s
I am using Cohen-Tanoudji notation and his coverage of Vand Der Waals forces, in Vol 2, page 1130 complement Cx1.