Fock state

A Fock state has specified occupation numbers. Applying creation operators to the vacuum constructs multiparticle momentum eigenstates.

A product of number states with equal fixed populations in two modes. Its total particle number is

2 N

. It differs from a pair of coherent states, whose number distributions fluctuate.

Relativistic normalization of a one-particle state ( $⟨ p ∣ q ⟩ = 2 E_{p} (2 π)^{3} δ^{3} (p - q)$ )

[a_{p}, a_{q}^{†}] = (2 π)^{3} δ^{3} (p - q)

∣ p ⟩ = 2 E_{p} a_{p}^{†} ∣0 ⟩

. Their inner product then has the displayed value. The associated completeness measure is

d^{3} p / ((2 π)^{3} 2 E_{p})

, the invariant positive-energy mass shell measure. Specifying this normalization prevents hidden external energy factors in a scattering amplitude.

The oscillator vacuum is annihilated by all annihilation operators. Acting with creation operators constructs Fock states. In single-string quantization this is the unexcited string, not the empty spacetime state.

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A Fock state, also known as a "number state," is a specific type of quantum state in quantum mechanics that represents a definite number of particles or excitations in a given system. The concept is particularly relevant in the context of quantum field theory and quantum optics, where it is used to describe states of bosonic fields, such as photons in a mode of a laser or phonons in a condensed matter system.