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In the boxed equation, how would you get the right hand side from the left hand side? We know that ##H(1,2) = H(2,1)##, but we first have to apply ##H(1,2)## to ##\psi(1,2)##, and then we would apply ##\hat{P}_{12}##; the result would not be ##H(2,1) \psi(2,1)##. ##\hat{P}_{12}## is the exchange operator and ##H(1,2)## is the hamiltonian.

Source: https://books.google.com.pk/books?i...inction as to which particle is which&f=false

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