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 following is in bra–ket notation: The number operator acts on Fock space. Let

be a Fock state drawn from a basis of the underlying Hilbert space of the Fock space. Given the corresponding creation and annihilation operators we define the number operator by

and we have

See also

• Harmonic oscillator

• Quantum harmonic oscillator

• Second quantization

• Quantum field theory

• Thermodynamics

• (-1)F

References

• Second quantization notes by Fradkin