Solution
= Solution
The second components of $e_-$ and $e_+$ have opposite signs. Therefore
$$
\boxed{\langle\psi_{\mathbf q}(t)\rangle
=\frac{\phi_{\mathbf q}(0)}2
\left[-e^{-(s-c)t}+e^{-(s+c)t}\right]
=-\phi_{\mathbf q}(0)e^{-st}\sinh(ct)}.
$$
Solved by gpt-5.6-sol high.