\left(x (\lambda + \lambda') + i y (\lambda - \lambda')\right)\right].$$ Some expectation values in the coherent state $|\lambda \lambda'\rangle$ are given by $$\begin{aligned}
&&\langle R_x \rangle = \sqrt{\frac{2}{M \omega}} \ \mbox{Re}\lambda', \
\Delta R_x = \frac{1}{\sqrt{2 M \omega}}, \nonumber \\
&&\langle R_y \rangle = \sqrt{\frac{2}{M \omega}} \ \mbox{Im}\lambda', \
\Delta R_y = \frac{1}{\sqrt{2 M \omega}}, \nonumber \\
&&\langle x - R_x \rangle = \sqrt{\frac{2}{M \omega}} \ \mbox{Re}\lambda, \
\Delta (x - R_x) = \frac{1}{\sqrt{2 M \omega}}, \nonumber \\
&&\langle y - R_y \rangle = - \sqrt{\frac{2}{M \omega}} \ \mbox{Im}\lambda, \
\Delta (y - R_y) = \frac{1}{\sqrt{2 M \omega}}, \nonumber \\
&&\langle M v_x \rangle =
\left\langle p_x + e A_x \right\rangle = 
\sqrt{2 M \omega} \ \mbox{Im}\lambda, \ 
\Delta(M v_x) = \sqrt{\frac{M \omega}{2}}, \nonumber \\
&&\langle M v_y \rangle =
\left\langle p_y + e A_y \right\rangle = 
\sqrt{2 M \omega} \ \mbox{Re}\lambda, \ 
\Delta(M v_y) = \sqrt{\frac{M \omega}{2}}, \nonumber \\
&&\langle H \rangle = \omega \left(|\lambda|^2 + \frac{1}{2}\right), \
\Delta H = \omega |\lambda|.\end{aligned}$$ Here $\Delta O = \sqrt{\langle O^2 \rangle - \langle O \rangle^2}$ describes the quantum uncertainty. In all cases $\Delta O/\langle O \rangle$ is proportional to $1/|\lambda|$ or $1/|\lambda'|$, which implies that the relative uncertainty goes to 