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Pauli's Principle says:

"The wavefunction of two identical fermions must be totally antisymmetric".

I know that, for a antisymmetric wavefunction,

$(-1)^L*(-1)^{S+1}*(-1)^{I+1}=-1$

"totally antisymmetric" means this relation or it means that these 3 relations:

$(-1)^L=-1$ and

$(-1)^{S+1}=-1$ and

$(-1)^{I+1}=-1$

must be verified simultaneusly?

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    $\begingroup$ What are $L$, $S$, $I$? $\endgroup$
    – Ruslan
    Commented Jun 27, 2014 at 19:18
  • $\begingroup$ @Ruslan L= angular momentum, S= spin, I= isospin $\endgroup$
    – sunrise
    Commented Jun 27, 2014 at 19:24

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It's the total product. The famous example is the spin of the deuteron. We have evidence that the two-nucleon isospin triplet with $I=1$ is unbound because we do not observe diprotons or dineutrons in nature, so we expect the deuteron to have isospin $I=0$. We know that the deuteron has positive parity, so we require $L$ even; by antisymmetry the deuteron must have spin $S=1$.

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