The Generalized Uncertainty Principle | Proof/Derivation

In this video, I finally prove/derive the Generalized Uncertainty Principle, using basic linear algebra identities such as the Schwarz Inequality as well as the properties of commutators and eigenvalue problems we discussed in the previous video (link: This video should conclude the mathematical prelude to Quantum Mechanics. Together with the previous 8 videos, it should prepare you for learning the subject. You could either use this video as a standalone (i.e. if you already know enough Quantum Mech and just want to learn how to prove the Uncertainty Principle) or as a continuation of my current introductory playlist. In the second case, if you don't understand what I mean by 'probability distribution on observable quantities' (which I discuss at the end), then don't worry too much, for I will be giving a n00b's intro to Quantum Mech later on. Being confused when starting out in Quantum Mech is fairly common, mainly because there's no standardized/sequential wa