Word Count : 256

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To show that for a Hamiltonian \[ \hat{H} = \frac{\hat{p}_x^2}{2m} + V(x) \] to commute with the time-reversal operator \(\hat{T}\), the potential function \(V(x)\) must be real, let's analyze the effect of time reversal on each term. ### Step 1: Time Reversal Operator Properties The time-reversal operator \(\hat{T}\) has the following __________ ________ _________ _____ ____ _____ ______ ____ _____ _______.
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