Operator in quantum mechanics
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, composed of single-particle states drawn from a
basis of the underlying Hilbert space of the Fock space. Given the corresponding
creation and annihilation operators and we define the number operator by
and we have
where is the number of particles in state . The above equality can be proven by noting that
then
See also
References