Solution
= Solution
In the ordered <basis> $|+\rangle,|-\rangle$, the transverse <magnetic field> produces
$$
V(t)=\mu_BB_1(\sigma_x\cos\omega t+\sigma_y\sin\omega t)
=\boxed{\hbar\gamma\begin{pmatrix}0&e^{-i\omega t}\\e^{i\omega t}&0\end{pmatrix}},\qquad\gamma=\frac{\mu_BB_1}{\hbar}.
$$
The off-diagonal complex exponentials follow directly from $\cos\omega t\mp i\sin\omega t$. This <matrix> is <Hermitian> at every time.