Solution
= Solution
Direct <differentiation> verifies the free-particle <Schrödinger equation>, so $V=0$. At $t=0$, normalisation of $Ae^{-x^2/2}$ gives $A=\pi^{-1/4}$. Symmetry gives $\langle x\rangle=0$, while Gaussian integration gives
$$
\Delta x=\sqrt{\frac{1+(\hbar t/m)^2}{2}}.
$$
Its growth shows wave-packet spreading and therefore a nonstationary state.