Uploaded December 2017 | Updated September 2026, 2 weeks ago
There's no better way to celebrate Christmas than with a 12 minute video on the Schrodinger Equation! In this lesson, I introduce Quantum Mechanics with a discussion on wavefunctions and the Schrodinger Equation (in 1-D). I show how wavefunctions can represent probability density functions (via the norm-squared), and discuss the significance of this representation.
I then introduce/revisit some basic Statistics concepts, and end the video with a proof of how the normalization of wavefunctions stays preserved with time.
Questions/requests? Ask in the comments!
Prereqs: This whole playlist: youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw
Lecture Notes: drive.google.com/open?id=1IA_theB0HyGh7JJMZ5nlCj8IYN0ap2ib
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
- Lisa Bouchard
NOTE: At around 11:30-11:45, I mention how the 'boundary' integrals have to approach zero at +/- infinity. This is true for square-integrable functions that come up in Physics. However, as one of the commenters pointed out, there are exceptions (i.e. square-integrable functions that don't approach zero at infinity). These exceptions aren't found in Physics though, so we'll ignore them, but I figure they're worth mentioning as a footnote.
There's no better way to celebrate Christmas than with a 12 minute video on the Schrodinger Equation! In this lesson, I introduce Quantum Mechanics with a discussion on wavefunctions and the Schrodinger Equation (in 1-D). I show how wavefunctions can represent probability density functions (via the norm-squared), and discuss the significance of this representation.
I then introduce/revisit some basic Statistics concepts, and end the video with a proof of how the normalization of wavefunctions stays preserved with time.
Questions/requests? Ask in the comments!
Prereqs: This whole playlist: youtube.com/playlist?list=PLdgVBOaXkb9Bv466YnyxslT4gIlSZdtjw
Lecture Notes: drive.google.com/open?id=1IA_theB0HyGh7JJMZ5nlCj8IYN0ap2ib
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
- Lisa Bouchard
NOTE: At around 11:30-11:45, I mention how the 'boundary' integrals have to approach zero at +/- infinity. This is true for square-integrable functions that come up in Physics. However, as one of the commenters pointed out, there are exceptions (i.e. square-integrable functions that don't approach zero at infinity). These exceptions aren't found in Physics though, so we'll ignore them, but I figure they're worth mentioning as a footnote.
