width is given by $$\begin{aligned}
\Delta \tau={\hbar \over \Delta E}={\Delta x \over v},~\Delta x={1 \over  \Delta k},~\Delta k={\Delta p \over \hbar }.\end{aligned}$$ In the above equations, the energy width $\Delta E$, time width $\delta \tau$, and position width $\Delta x$ are determined using the momentum width $\Delta p$.

The position of the wave packet also varies with time in a manner that follows a classical trajectory of the velocity given by the central value of the momentum. Furthermore, the wave packet spreads with time with a speed that depends on the mass and initial size.

The other feature of the wave packets can be observed in a momentum correlation, $$\begin{aligned}
C({\vec p}_1,{\vec p}_2)=(\langle {\vec p}_1|\alpha \rangle )(\langle {\vec p}_2|\alpha  \rangle)^{*}=\langle {\vec p}_1|\alpha \rangle \langle \alpha|{\vec p}_2 \rangle,
\label{correlation-wave packet}\end{aligned}$$ where the state $ | \alpha \rangle $ is one state described using a wave packet and $ | {\vec p} \rangle $ is a momentum eigenstate. If the state $| \alpha \rangle $ is a momentum state $|{\vec q} \rangle $, then we have $$\begin{aligned}
C_0({\vec p}_1,{\vec p}_2)=(\langle {\vec p}_1|\vec q \rangle )(\langle {\vec p}_2|
{\vec q}'  \rangle)^{*}=\delta ({\vec p}_1-{\vec q})\delta ({\vec p}_2-{\vec q}),\end{aligned}$$ and $C_0({\vec p}_1,{\vec p}_2)$ is proportional 