Solution
= Solution
Projection onto the antisymmetric <quantum superposition> gives amplitude $\tfrac12(e^{-iE_1t/\hbar}-e^{-iE_2t/\hbar})$. Its squared modulus is
$$
\boxed{P_{+\to-}(t)=\sin^2\left(\frac{(E_2-E_1)t}{2\hbar}\right).}
$$
It vanishes initially, reaches one at a half-recurrence time, and returns to zero after $\tau$. This interference depends on a relative phase even though each energy-eigenstate population and the mean <energy> remain constant.