Exact mathematical details to visualize:Quantum Gaussian Wave Packet Identity: The identity is: \psi(x,t) = \frac{1}{\sigma^{1/2}\pi^{1/4}}\...

Exact mathematical details to visualize:Quantum Gaussian Wave Packet Identity: The identity is: \psi(x,t) = \frac{1}{\sigma^{1/2}\pi^{1/4}}\frac{1}{\sqrt{1+\frac{i\hbar t}{m\sigma^2}}} \times \exp \left(-\frac{1}{2\left(\sigma^2+\frac{i\hbar t}{m} \right)}\left(x^2-2i\sigma^2\bar{p}/\hbar\left(x-\frac{\bar{p}}{2m}t\right) ...