Griffiths QM problem 2.40 (3rd ed): Checking Uncertainty Principle for Traveling Wave Packet (HARD)

Описание: In this video, I will solve problem 2.40 as it appears in the 3rd edition of Griffiths introduction to Quantum Mechanics. The objective states:
In problem 2.22 you analyzed the stationary Gaussian free particle wave packet. Now solve the same problem for the traveling Gaussian wave packet, starting with the initial wave function: psi(x,0)=Ae^-ax^2 e^ilx
a) In particular, we need to normalizae the wave function
b) Find psi(x,t) by completing the square
c) Find |psi(x,t)|^2 (probability density)
d) find uncertainties of x, x^2,p,p^2, sigma x and sigma p
e) Check the uncertainty principle

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My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00:00 Introducing the problem
00:01:30 Explaining the procedure
00:03:03 a) Normalizing the wave function
00:05:10 b) Finding phi(k)
00:13:50 b) finding Psi(x,t)
00:32:00 c) Finding |psi(x,t)|^2 (probability density)
00:44:30 d) Finding the expectation value of x
00:49:40 d) Finding the expectation value of p
00:50:30 d) Finding the expectation value of x^2
00:59:20 d) Finding the expectation value of p^2
01:14:10 d) Finding the uncertainties and e) checking the Uncertainty principle