Griffiths QM 1.14 Solution (HARD PROBLEM) - Expectation Values for Gaussian wavefunction

In this video I will solve problem 1.14 as it appears in the 3rd edition of Griffiths Introduction to Quantum mechanics. The problem states:
A particle of mass m is in the state ....
a) Find A
b) For what potential energy function V(x) does psi satisfy the schrödinger equation?
c) Calculate the expectation values of x, x^2, p and p^2
d) Find the uncertainties and check that it is consistent with the uncertainty principle

If you enjoy my content, please consider checking out my Patreon!
www.patreon.com/nickheumann

Also, consider subscribing and following me on my socials!

twitter: twitter.com/nickheumann
Instagram: instagram.com/nicolasheumann
twitch: www.twitch.tv/nickheumann

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 Introducing the Problem
00:45 a) Normalizing the wavefunction
03:15 b) Finding the potential
08:42 c) Finding the expectation value of x
10:02 c) Finding the expectation value of x squared
13:57 c) Finding the expectation value of p
14:25 c) Finding the expectation value of p squared
17:55 d) Finding the uncertainties and check Heisenberg Principle