Time-reversal symmetry in quantum mechanics
= Time-reversal symmetry in quantum mechanics
A time-reversal operator $T$ intertwines forward and backward evolution:
$$
U(t)T=TU(-t).
$$
It must be antiunitary in ordinary quantum mechanics. Its conjugate linearity sends $i$ to $-i$, allowing it to commute with a time-reversal-invariant Hamiltonian rather than reversing the sign of its energy.