If I have three fermions in states v, y', and " (a) Construct a fully asymmetric state V (F1, 72, 73) = v (7i) V' (F2) 4" (F3) +... in which you include every permutation of the three particles (how many are there?) with the appropriate sign for each. Don't worry about normalization. (b) Demonstrate explicitly that this goes zero if " = ' (i.e. if any two of the three states are the same).
If I have three fermions in states v, y', and " (a) Construct a fully asymmetric state V (F1, 72, 73) = v (7i) V' (F2) 4" (F3) +... in which you include every permutation of the three particles (how many are there?) with the appropriate sign for each. Don't worry about normalization. (b) Demonstrate explicitly that this goes zero if " = ' (i.e. if any two of the three states are the same).
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Transcribed Image Text:2. If I have three fermions in states , s', and "
(a) Construct a fully asymmetric state
V (F1, 72, T3) = v (F1) V' (F2) v" (F3) + ..
in which you include every permutation of the three particles (how many are there?)
with the appropriate sign for each. Don't worry about normalization.
(b) Demonstrate explicitly that this goes zero if " = ' (i.e. if any two of the three states
are the same).
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