Introduction to Quantum Mechanics: Schrodinger Equation

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!

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.

[yym]

In korea now, due to covid19 many universities are taking lectures online. (Youtube uploaded lecture, lectures using zoom meating, etc) and you are much better than my professor.

[mahimajerushasingh]

Thank you for referring to Quantum Mechanics as "not very difficult" and "not very different", it kinda takes away the chills that I get thinking about this subject :)

[vismithanadig]

I've been on the lookout for precise videos like this, and this is THE BEST i have found! It's so easy to understand, the derivation is done in detail without missing any steps. Being a biology student, i'm taking a stat phy course to get a better understanding of the quantum world. The math wasnt that hard. Students are very intimidated by professors teaching this subject. The way you treat this as something that's not complex but can be understood in parts and with different viewpoints is encouraging!

[chinkitkit]

Thank you so much, sir.
Your video is clear cut as always and direct.
The explanation is definitely great.
Thanks in million.

[clearz]

This sounds to me like someone created a Text to Speech based on Khan's voice!

[SJSINGH]

Excellent way of explaining such a complex topic. Grateful. Thanks.

[FridgeGames]

this is a very good introduction to the Schrodinger equation !

[eamonnsiocain]

My Classical Mechanics 'Glory Days?' LOL!

[physics_enthusiast_Soorya]

Wow! I learnt something I didn't know!

It's about the delta function..

It's very interesting, thanks ✨️✨️

[kelvin]

thx to this video!!!
utube is my real prof

[samiaboudiab]

Although I only know basics physics, the explanation provided in this video gave a real understanding of the Schrodinger equation in less than 15 minutes.  I am simply left speechless.  Thank you so much for such an insightful video and for your genuine desire pass on your knowledge.

[AdvancedGT]

You talk like robot, but your explanation is amazing. Thank you

[elamvaluthis]

Crystal clear explanation thank you sir.

[ozzyfromspace]

As always, awesome presentation Faculty of Khan! Thanks, and happy holidays. :)

[richos]

I've come to learn about quantum mechanics after watching Oppenheimer

[zeekthegeek]

love these funny yet informative video, its like you're tricking me to learn without me knowing lol

[TomAustinIII]

Saying "measurement changes particle wave function, " is entertaining. It's a very entertaining concept the more vague you remain. A more accurate statement would be that seeing requires photons and the photons hit the electrons and alter their motion. Any measurable thing that that you bounce off of the electron alters the motion of the electron. That's all it is. conservation of momentum...

[ZaChaudhry]

you are Rock sir, You helped me a lot in my Phsics course. Will You please make lectures on Perterbation theory and WKB approximation.

[RmA_]

love it love it love it very clearly explained thank you

[OnTheThirdDay]

Thank you.
Just a remark, just because \psi is square integrable, that does not mean that it converges to zero. It means that if the function is uniformly continuous, but otherwise not.

Perhaps, one would argue that state functions that do not have \lim_{ |x| \to \infty } f(x) = 0 are not physical.

An example is the function f(x) = n on the interval [n, n+1/n^4). We then see that \int |f(x)|^2 dx = \sum_{n > 0} n^2/n^4, which is finite.
This f is not continuous, but one can (using smooth step functions instead of normal step function) find a smooth function that has the property that f(x) converges to infinity as x goes to infinity but is still square integrable.