Exchange Symmetry
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High Quality Content by WIKIPEDIA articles! Exchange symmetry is derived from a fundamental postulate of quantum statistics, which states that no observable physical quantity should change after exchanging two identical particles. It states that because all observables are proportional to for a system of identical particles, the wave function must either remain the same or change sign upon such an exchange. Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 360 degrees, the symmetric nature of the wave function depends on the partic...
High Quality Content by WIKIPEDIA articles! Exchange symmetry is derived from a fundamental postulate of quantum statistics, which states that no observable physical quantity should change after exchanging two identical particles. It states that because all observables are proportional to for a system of identical particles, the wave function must either remain the same or change sign upon such an exchange. Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 360 degrees, the symmetric nature of the wave function depends on the particle's spin after the rotation operator is applied to it. Integer spin particles do not change the sign of their wave function upon a 360 degree rotation therefore the sign of the wave function of the entire system does not change. Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin-statistics theorem). Particles for which the wave function does not change sign upon exchange are called bosons, or particles with a symmetric wave function.
