Often one wants to replace a fully microscopic theory by a more manageable, effective theory. This can be done in two steps as follows:
First step: divide the system under consideration into constituent entities (subsystems).
Second step: find a description in terms of effective potentials between the constituent entities while trying to stay as close as possible to the full microscopic theory.
Example 1: Two molecules of size
at distance
. Full system = all electrons and all nuclei together. Subsystems: the two molecules. This is a `good description' as long as each molecule is recognizable as one unity. Separation of a) length and b) energy scales is important here: a)
; b) the force between the molecules is not strong enough to destroy them, e.g. by ripping out electrons.
Example 2: Nuclear physics. Underlying microscopic theory is QCD. Use effective description of system (nucleus) in terms of effective potentials between constituent nucleons (neutrons and protons).
Example 3: (classical or quantum) statistical mechanics, e.g. calculation of the free energy of a system of atomsor a system of molecules (gas/liquid/solid).
3a) Cohesive energy of solids, cf. Ashcroft/Mermin `Solid State Physics' [9] ch. 20.
3b) Dispersion forces in colloids, cf. Mahanty/Ninham `Dispersion Forces' [10].