Uploaded November 2017 | Updated September 2026, 2 weeks ago
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: youtube.com/watch?v=-h2lU2FXy48).
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 way of teaching it (i.e. you'll be confused regardless of how you start learning it).
Still, if something isn't clear to you or if you have questions/feedback, ask in the comments!
NOTE: When I define deltaAhat/deltaBhat, it's assumed that we're subtracting the expectation value *times the identity operator* from the Ahat/Bhat operators. Obviously, it's incorrect to take away a scalar from an operator without first multiplying that scalar with another operator.
Prereqs: Everything before this video on my playlist so far - youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw
Lecture Notes: drive.google.com/open?id=1cCcwXkgD-jJxJxaivmRkrAy3ElEc2813
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan?lang=en
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
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: youtube.com/watch?v=-h2lU2FXy48).
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 way of teaching it (i.e. you'll be confused regardless of how you start learning it).
Still, if something isn't clear to you or if you have questions/feedback, ask in the comments!
NOTE: When I define deltaAhat/deltaBhat, it's assumed that we're subtracting the expectation value *times the identity operator* from the Ahat/Bhat operators. Obviously, it's incorrect to take away a scalar from an operator without first multiplying that scalar with another operator.
Prereqs: Everything before this video on my playlist so far - youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw
Lecture Notes: drive.google.com/open?id=1cCcwXkgD-jJxJxaivmRkrAy3ElEc2813
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan?lang=en
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
