The annihilation and creation operator description has also been useful to analyze classical reaction diffusion equations, such as the situation when a gas of molecules A diffuse and interact on contact, forming an inert product: A + A → → ∅ ∅ . To see how this kind of reaction can be described by the annihilation and creation operator formalism, consider n i particles at a site i on a one dimensional lattice. Each particle moves to the right or left with a certain probability, and each pair of particles at the same site annihilates each other with a certain other probability.