Particle number operator
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The number operator acts on Fock space. Let be a Fock state, composed of single-particle states formula_2 drawn from a basis of the underlying Hilbert space of the Fock space. Given the corresponding creation and annihilation operators formula_3 and formula_4 we define the number operator by and we have where formula_7 is the number of particles in state formula_2. The above equality can be proven by noting that then