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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Exchange operator ： ウィキペディア英語版 Exchange operator In quantum mechanics, the exchange operator $\backslash hat$ is a quantum mechanical operator that acts on states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state $\backslash left|x\_1,\; x\_2\backslash right\backslash rangle$. Since the particles are identical, the notion of exchange symmetry requires that the exchange operator be unitary. ==Construction== (詳細はdimensions, the exchange operator can represent a literal exchange of the positions of the pair of particles by motion of the particles in an adiabatic process, with all other particles held fixed. Such motion is often not carried out in practice. Rather, the operation is treated as a "what if" similar to a parity inversion or time reversal operation. Consider two repeated operations of such a particle exchange: :$\backslash hat^2\backslash left|x\_1,\; x\_2\backslash right\backslash rangle\; =\; \backslash hat\backslash left|x\_2,\; x\_1\backslash right\backslash rangle\; =\; \backslash left|x\_1,\; x\_2\backslash right\backslash rangle$ Therefore $\backslash hat$ is not only unitary but also an operator square root of 1, which leaves the possibilities :$\backslash hat\backslash left|x\_1,\; x\_2\backslash right\backslash rangle\; =\; \backslash pm\; \backslash left|x\_1,\; x\_2\backslash right\backslash rangle\backslash ,.$ Both signs are realized in nature. Particles satisfying the case of +1 are called ''bosons'', and particles satisfying the case of −1 are called ''fermions''. The spin–statistics theorem dictates that all particles with integer spin are bosons whereas all particles with half-integer spin are fermions. The exchange operator commutes with the Hamiltonian and is therefore a conserved quantity. Therefore it is always possible and usually most convenient to choose a basis in which the states are eigenstates of the exchange operator. Such a state is either completely symmetric under exchange of all identical bosons or completely antisymmetric under exchange of all identical fermions of the system. To do so for fermions, for example, the antisymmetrizer builds such a completely antisymmetric state. In 2 dimensions, the adiabatic exchange of particles is not necessarily possible. Instead, the eigenvalues of the exchange operator may be complex phase factors (in which case $\backslash hat$ is not Hermitian), see anyon for this case. The exchange operator is not well defined in a strictly 1-dimensional system, though there are constructions of 1-dimensional networks that behave as effective 2-dimensional systems. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exchange operator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.