The Heisenberg Uncertainty Principle: Proof/Explanation! 

In this video, I derive and discuss the Heisenberg Uncertainty Principle, perhaps one of the most famous relationships in Quantum Mechanics. I start by using the Generalized Uncertainty Principle (derived here: • The Generalized Uncert... ) to determine the commutator of the position and momentum operators whose expressions I found in the previous video (link: • Position and Momentum ... ).
Once I derive the Heisenberg Uncertainty Principle, I devote much of the video to explaining what it means - *that it's a statement on the fundamental nature of quantum mechanical particles which arises from certain mathematical principles (e.g. Fourier Transforms) describing those particles*. In the video, I state that the Heisenberg Uncertainty Principle 'is a consequence of mathematics', but keep in mind that this mathematics is used to model quantum mechanical particles. Thus, in the context of Quantum Mechanics, the Heisenberg Uncertainty Principle is a physical fact that can be derived mathematically (that's what I mean when I say 'consequence of mathematics').
Towards the end of the video, I emphasize that the Uncertainty Principle is NOT a statement about observer-induced limitations on measurements; that's the Observer Effect. The Heisenberg Uncertainty Principle is rather difficult to wrap one's head around, at least at first, so I encourage you to ask questions and comment down below!
Prerequisites: All the previous videos in this playlist (Playlist 1: ru-vid.com?list..., and all the videos in this playlist: • Quantum Mechanics: Mat... .
Lecture Notes: drive.google.com/open?id=1S7B...
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EDIT: The deBroglie formula at 6:40 should have hbar instead of h.