Definition
A more mathematical definition is that Fock states are those elements of a Fock space which are eigenstates of the particle number operator. Elements of a Fock space which are superpositions of states of differing particle number (and thus not eigenstates of the number operator) are, therefore, not Fock states. Thus, not all elements of a Fock space are referred to as "Fock states."
If we limit to a single mode for simplicity (doing so we formally describe a mere harmonic oscillator), a Fock state is of the type with n an integer value. This means that there are n quanta of excitation in the mode. corresponds to the ground state (no excitation). It is different from 0, which is the null vector.
Fock states form the most convenient basis of the Fock space. They are defined to obey the following relations in the bosonic algebra:
with (resp. ) the annihilation (resp. creation) bose operator. Similar relations hold for fermionic algebra.
This allows to check that and, i.e., that measuring the number of particles in a Fock state returns always a definite value with no fluctuation.
Read more about this topic: Fock State
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