Uploaded March 2018 | Updated September 2026, 2 weeks ago
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: youtube.com/watch?v=qgkWUuqoSVM) to determine the commutator of the position and momentum operators whose expressions I found in the previous video (link: youtube.com/watch?v=Egu4i8umpoM).
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: youtube.com/playlist?list=PLdgVBOaXkb9AtG88OsK_c8FDEBDLCC6_9), and all the videos in this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw.
Lecture Notes: drive.google.com/open?id=1S7BUUttlepXFHBaLAmryWqzXy8JhXd5k
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- Justin Hill
- Marcin Maciejewski
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
EDIT: The deBroglie formula at 6:40 should have hbar instead of h.
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: youtube.com/watch?v=qgkWUuqoSVM) to determine the commutator of the position and momentum operators whose expressions I found in the previous video (link: youtube.com/watch?v=Egu4i8umpoM).
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: youtube.com/playlist?list=PLdgVBOaXkb9AtG88OsK_c8FDEBDLCC6_9), and all the videos in this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw.
Lecture Notes: drive.google.com/open?id=1S7BUUttlepXFHBaLAmryWqzXy8JhXd5k
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- Justin Hill
- Marcin Maciejewski
- Jacob Soares
- Yenyo Pal
- Chi
- Lisa Bouchard
EDIT: The deBroglie formula at 6:40 should have hbar instead of h.
