= Quantum time-reversal operator
{title2=$\hat T$}
A quantum time-reversal operator is an <antiunitary operator> reversing spatial <momentum> and <angular momentum>. For a time-reversal-invariant <Hamiltonian operator>, its conjugation of $i$ makes it intertwine forward and backward <unitary time evolution> without reversing the <energy> spectrum. A scalar <momentum eigenstate> may transform as $\hat T|\boldsymbol p\rangle=e^{i\chi(\boldsymbol p)}|-\boldsymbol p\rangle$. With unit-modulus phases and a complete normalized basis, expansion of arbitrary states proves <antiunitarity>.
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