这是一份umass麻省大学 MATH 532H作业代写的成功案例
(a) Perturbation associated with $\Delta \mathrm{h}{a \perp}^{\mathrm{dc}}\left(\omega{\mathrm{p}}=\omega\right)$ :
$$
\left(\begin{array}{c}
\tilde{b}{1} \ \tilde{b}{2}
\end{array}\right)=\Delta \mathrm{h}{a \perp}^{\mathrm{dc}}\left(\begin{array}{c} \cos \theta{0} \
\mathrm{i}
\end{array}\right) \mathrm{e}^{-\mathrm{i}\left(\phi_{0}+\psi_{\mathrm{d} c}\right)}
$$
(b) Perturbation associated with $\Delta \mathrm{h}{a \perp}^{\mathrm{rf}}\left(\omega{\mathrm{p}}=2 \omega\right)$ :
$$
\left(\begin{array}{l}
\tilde{b}{1} \ \tilde{b}{2}
\end{array}\right)=\Delta \mathrm{h}{a \perp}^{\mathrm{rf}}\left(\begin{array}{c} \cos \theta{0} \
\mathrm{i}
\end{array}\right) \mathrm{e}^{\mathrm{i}\left(\psi_{\perp}-\phi_{0}\right)}
$$
(c) Perturbation associated with $\Delta \mathrm{h}{a z}^{\mathrm{rf}}\left(\omega{\mathrm{p}}=\omega\right)$ :
$$
\left(\begin{array}{l}
\tilde{b}{1} \ \tilde{b}{2}
\end{array}\right)=\Delta \mathrm{h}{a z}^{\mathrm{rf}}\left(\begin{array}{c} -\sin \theta{0} \
0
\end{array}\right) \mathrm{e}^{\mathrm{i} \psi{ }^{\mathrm{x}}}
$$
(d) Perturbation associated with $\Delta \kappa\left(\omega_{\mathrm{p}}=\omega\right)$ :
$$
\left(\begin{array}{l}
\tilde{b}{1} \ \tilde{b}{2}
\end{array}\right)=\Delta \kappa\left(\begin{array}{c}
\cos 2 \theta_{0} \
i \cos \theta_{0}
\end{array}\right) \mathrm{e}^{-\mathrm{i}\left(\phi_{0}+\psi_{\mathrm{AN}}\right)}
$$
MATH 532H COURSE NOTES ：
Let us introduce the new amplitudes $\left(z_{q 1}, z_{q_{2}}\right)$ defined by the formula:
$$
\left(\begin{array}{l}
c_{q 1} \
c_{q 2}
\end{array}\right)=\Pi_{q}(t)\left(\begin{array}{l}
z_{q 1} \
z_{q 2}
\end{array}\right)
$$
By substituting this expression into Eq. and by taking account of Eq. one finds:
$$
\frac{\mathrm{d}}{\mathrm{d} t}\left(\begin{array}{l}
z_{q 1} \
z_{q 2}
\end{array}\right)=\Omega_{q}\left(\begin{array}{l}
z_{q 1} \
z_{q 2}
\end{array}\right),
$$
where $\Omega_{q}$ is the time-independent matrix from Eq. (8.39). In terms of the discriminant:
$$
\omega_{q}^{2}=\operatorname{det} \Omega_{q}-\frac{\left(\operatorname{tr} \Omega_{q}\right)^{2}}{4}
$$