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Let us consider two fermions whose spin state wave functions are certain (normalized) ##\psi_{1}## and ##\psi_{2}##.

So the overall normalized spin state wave function of this system is of the form:

##\psi = (1/\sqrt{2})(\psi_{1} \psi_{2} - \psi_{2} \psi_{1})##

Is there any difference between calculating the total square spin operator ##\hat S^{2}##eigenvalueand theaveragevalue of ##S^{2}##?

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# Average value of square spin

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