Hamaker theory

The interaction of two bodies is then treated as the pairwise interaction of a set of N molecules at positions: R_i {i:1,2,... ...,N}. The distance between the molecules i and j is then:

${\displaystyle R_{ij}=|R_i-R_j|}$

The interaction energy of the system is taken to be:

${\displaystyle V_{\mathrm{i}\mathrm{n}\mathrm{t}}^{1,2,...N}=\frac{1}{2}\sum _{i=0}^{\mathbb{N}}\sum _{j=0(\ne i)}^{\mathbb{N}}{V}_{\mathrm{i}\mathrm{n}\mathrm{t}}^{ij}(R_{ij})}$

where ${\displaystyle V_{\mathrm{i}\mathrm{n}\mathrm{t}}^{ij}}$ is the interaction of molecules i and j in the absence of the influence of other molecules.

The theory is however only an approximation which assumes that the interactions can be treated independently, the theory must also be adjusted to take into account quantum perturbation theory.