5.6.1 Solution ident-a
Check that indeed any linear combination of the triplet states is unchanged under particle exchange.
In the notations of the previous section, the most general linear combination of the triplet states takes the form:
or writing out their definitions as found there,
Exchanging the two particles involved means to interchange the order of each pair of arrows, since by definition the first arrow refers to particle 1 and the second to particle 2. A look at the expression above shows that such an interchange of order does absolutely nothing to these states.