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I am trying to understand the concept of symmetric and antisymmetric wave functions in QM.

Now the Griffiths and other textbooks I have introduce the exchange operator as an operator that switches two particles in a given two particle wave function.

But then an eigenvalue equation is introduced for the exchange operator with eigenvalues +1 or -1

And finally the original wave function is said to equal the one with the switched particles multiplied by a +1 or a -1.

Now I don't understand how this statement can be made because the switched wave function can not be an eigenfunction of the exchange operator because it is switched and not the original wave function so it does not satisfy the eigenvalue equation for the exchange operator.

Thanks for your Help!! =)

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# Exchange operator

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