zero in the classical limit.

Just as in the ordinary harmonic oscillator, the time-dependent Schrödinger equation $i {\partial}_t |\Psi(t)\rangle = H |\Psi(t)\rangle$ with an initial coherent state $|\Psi(0)\rangle = |\lambda(0) \lambda' \rangle$ is (up to an irrelevant phase) solved by $|\lambda(t) \lambda'\rangle$ with $$\lambda(t) = \lambda(0) \exp(- i \omega t).$$ As expected, the state remains coherent during its time-evolution. In particular, this implies $$\begin{aligned}
&&\langle x - R_x \rangle(t) = 
\frac{|\lambda|}{\sqrt{2 M \omega}} \cos(\omega t), \
\langle M v_x \rangle(t) = - \sqrt{2 M \omega} \ |\lambda| \sin(\omega t), 
\nonumber \\
&&\langle y - R_y \rangle(t) = 
\frac{|\lambda|}{\sqrt{2 M \omega}} \sin(\omega t), \
\langle M v_y \rangle(t) = \sqrt{2 M \omega} \ |\lambda| \cos(\omega t).\end{aligned}$$ Hence, the coherent state represents a Gaussian wave packet moving around a circular cyclotron orbit just like a classical particle. This is obvious from the coordinate representation of the probability density $$\begin{aligned}
&&|\langle \vec x|\Psi(t)\rangle|^2 = A \exp\left(- \frac{M \omega}{2}
\left[(x - \langle x \rangle(t))^2 + 
(y - \langle y \rangle(t))^2\right]\right), \nonumber \\
&&\langle x \rangle(t) = \langle R_x \rangle + 
\sqrt{\frac{2}{M \omega}} |\lambda| \cos(\omega t), \
\langle y \rangle(t) = \langle R_y \rangle + 
\sqrt{\frac{2}{M \omega}} |\lambda| \sin(\omega t).\end{aligned}$$

It is interesting to note 