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Fock states : ウィキペディア英語版
Fock state
In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics.
The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions.
==Definition==
One specifies a multiparticle state of N non-interacting identical particles by writing the state as a sum of tensor products of N one-particle states. The tensor products must be alternating products or symmetric products of the underlying one-particle Hilbert space according to whether the particles are fermions or bosons. If the number of particles is variable, one constructs Fock space as the direct sum of the tensor product Hilbert spaces for each particle number.
Then it is possible to specify the same state in a new notation, the occupancy number notation, by specifying the number of particles in each possible one-particle state.
Let ki be an orthonormal basis of states in the underlying one-particle Hilbert space. This induces a corresponding basis of the Fock space called the "occupancy number basis". A quantum state in the Fock space is called a Fock state if it is an element of the occupancy number basis.
A Fock state satisfies an important criterion: for each ''i'', the state is an eigenstate of the particle number operator \widehat} corresponding to the ''i''-th elementary state ki. The corresponding eigenvalue gives the number of particles in the state. This criterion nearly defines the Fock states (one must in addition select a phase factor).
A given Fock state is denoted by |n__1},n__2},..n__i}...\rangle. In this expression, n__i} denotes number of particles in the i-th state ki, and the
particle number operator for the i-th state, \widehat}, acts on the Fock state in the following way:
\widehat}|n__1},n__2},..n__i}...\rangle=n__i}|n__1},n__2},..n__i}...\rangle
Hence the Fock state is an eigenstate of the number operator with eigenvalue n__i}.
Fock states form the most convenient basis of a Fock space. Elements of a Fock space which are superpositions of states of differing particle number (and thus not eigenstates of the number operator) are not Fock states. Thus, not all elements of a Fock space are referred to as "Fock states".
The definition of Fock state ensures that (\widehat)=0, i.e., measuring the number of particles in a Fock state always returns a definite value with no fluctuation. Here
:\widehat=\sum_i \widehat}.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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