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.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 3 / vii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-353/3/vii/solution