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I am stuck on how to connect the ideas that two spin half particles must form a anti-symmetric wavefunction. Is there a proof on how to show that two spin one half particles must form a anti-symmetric wavefunction?

\begin{align} \Psi(x_1,x_2) = \Psi_1(x_2) \Psi_2(x_1) - \Psi_2(x_1) \Psi_1(x_2) \end{align}

This would indeed prove that spin half particles must obey the Pauli Exclusion Principle, because if two fermions were in the same state, then the wavefunction would equal zero.

linuxfreebird
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    Could you be looking for the spin-statistics theorem? – ACuriousMind Jul 13 '14 at 22:07
  • @ACuriousMind I think so. All though I do not have enough money to buy the paper : http://link.springer.com/article/10.1007%2Fs10701-009-9351-4 . Sorry. – linuxfreebird Jul 13 '14 at 22:15
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    I don't think you need to buy any papers. The Wikipedia article itself already offers a full proof of the theorem. – ACuriousMind Jul 13 '14 at 22:35
  • There is a discussion in Peskin and Schroeder for the specific example of spin one half. If you don't have the money for the book, you could try a library. – Robin Ekman Jul 13 '14 at 22:38
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    If you're only working with first quantization (not QFT), you can't actually prove it. In that theoretical framework it's a principle in the real sense of the word. Introducing special relativity and allowing second quantization is needed to prove it from other first principles. – ticster Jul 13 '14 at 22:41

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