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## Homework Statement

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Let P be the exchange operator:

Pψ(1,2) = ψ(2,1)

How can I prove that the exchange operator is hermitian?

I want to prove that <φ|Pψ> = <Pφ|ψ>

## Homework Equations

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<φ|Pψ> = <Pφ|ψ> must be true if the operator is hermitian.

## The Attempt at a Solution

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<φ(1,2) | P ψ(1,2) > = ∫φ*(1,2) P ψ(1,2) dτ = ∫φ*(1,2) ψ(2,1) dτ

<P φ(1,2) | ψ(1,2)> = ∫P* φ*(1,2) ψ(1,2) dτ = ∫φ*(2,1) ψ(1,2) dτ