Consider a particle of mass $m$ under an harmonic potential, $V=\frac12 kx^2$. The coherence states
$$\psi_\alpha=e^{-{{1}\over{2}}|\alpha|^2}\sum_{n=0}^\infty{{\alpha^n}\over{\sqrt{n!}}}\psi_n$$
where $\psi_n$ are the energy eigenfunctions, are eigenfunctions of the annihilation operator ($â \psi_\alpha =\alpha\psi_\alpha$). How could I determine the standard deviation of the position and momentum of the particle in state $\psi_\alpha$?
