Consider a superposition of two Gaussian wave packets with the same momentum \(p_{0}\), initially (at time \(t_{0}\) ) at the same position \(x_{0}\), but with different variances, \(\sigma_{1}=d_{1}\) and \(\sigma_{2}=d_{2}\). Calculate \(\left\langle(\Delta x)^{2}\rightangle\) and \(\left\langle(\Delta p)^{2}\rightangle\), and check the Heisenberg uncertainty relation, at time \(t_{0}\).