Fock state

A Fock state, in quantum mechanics, is any state of the Fock space with a well-defined number of particles in each state. The name is for V. A. Fock.

Related Topics:
Quantum mechanics - Fock space - Particle - V. A. Fock

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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 |n> with n an integer value. This means that there are n quanta of excitation in the mode. |0> corresponds to the ground state (no excitation). It is different from 0 which is the null vector.

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Fock states form the most convenient basis of the Fock space. They are defined to obey the following relations in the bosonic algebra:

Related Topics:
Basis - Bosonic

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:a^{dagger}|n angle=sqrt{n+1}|n+1 angle

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:a|n angle=sqrt{n}|n-1 angle

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:|n angle={1oversqrt{n!}}(a^{dagger})^n|0 angle

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with a (resp. a†) the annihilation (resp. creation) bose operator. Similar relations hold for fermionic algebra.

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This allows to check that =n and Var(a†a)=0, i.e., that measuring the number of particles a†a in a Fock state returns always a definite value with no fluctuation.

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