What is the Schrödinger Equation? A basic introduction to Quantum Mechanics

This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wave-function is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is shown that a linear superposition of energy eigenstates leads to non-stationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed.

References:
Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick (Motivating the structure of the Schrodinger equation)
Introduction to Quantum Mechanics - Griffiths and Schroeter (Examples of expectation values and superposition of states).
Introduction to Quantum Mechanics - Phillips
Vibrations and Waves - King
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais

[turtledruid]

I think it's really a testament to your explanation skills that the Schrodinger equation seems like it's the obvious solution once you've seen it. It was, of course, not obvious, even to Schrodinger himself. The time and effort you must put into these videos is astounding, and I thoroughly enjoy watching them. Great work!

[galangal]

Having taken a physics degree many decades ago may I congratulate you on such an excellent presentation.

[Theunit]

In all of my university courses, textbooks, websites, and videos I've indulged to learn intro QM, this is easily the best overview with the clearest and most well-put explanations and motivations. Thank you.

[robandsharonseddon-smith]

Outstanding work. I somehow managed to understand all of it, whilst understanding none of it at each stage. Coming from a non-physics background, and with only a limited understanding of calculus, to be able to carry a viewer with my limited ability along is testament to your superb communication. Thank you.

[kidus]

I love how you start building up from the historical background, something we don’t see often. I hope you will upload more often❤️

[dutonic]

I've spent the last few days watching through this and filling up over 25 pages with notes. I would always pause and see if I could derive/solve the problems every time. I would get stuck about half the time and when I caved and watched your walkthrough I would frequently be like "You can do that?!?!?! No way!!". Watching the solutions to the time independent schrodinger equation match up with my undergrad chemistry education was such a mind blowing moment. When I finally understood why energy was quantized was a big aha moment for me. But then when you pulled up the graph of the energy levels in the box and the probability distributions, I flipped out. What an amazing video. I cannot thank you enough for this amazing content. I can't wait to watch every video on your channel many times over.

[ss_avsmt]

I am doing my doctorate in Engineering, and studying theoretical physics is my all time favourite hobby. I am going to derive all these myself now. Many thanks for creating this wonderful presentation.

[KonovDS]

It always amazed me, that when I was in school everything about quantum mechanics was a synonym of something very difficult and counterintuitive, thanks to the pop culture and popular science articles/videos on youtube. After studying in university it turned out to be much easier, espesially considering that classcial mechanics is not that simple either. If i saw this video 5 years ago I would have understood that fact earlier. Thank you for this clear and neat explonation.

[berryesseen]

What I like the most about this video is that he always kept the proper math behind the theory, and all the are clearly justified. Most Youtube videos on quantum mechanics don't go this deep into the math, so many things like the probability interpretation of the wave function become vague. This video does a great job to fix this. I think that any Freshman with a little bit of calculus background can understand what is going on in this video.

[ThatCrazyKid]

I cannot express how incredible this video is. Thank you so much for the work you do, I've never seen anyone on YouTube deliver the _intuition_ behind the theory, both the derivation of the maths as well as the implications and applications of said math on physical results. And to do it in such a clear and concise way that you can follow along step by step, it really is an impressive feat. I also really appreciate the history of how these theories came to be, it is such an important part of physics that often gets left out when it has an entire story to tell. Cheers mate.

[chuckstarwar]

you did a great job. Nine out of ten physics professors today just brings out the " Schrödinger equation", on board. This is exactly how the Quantum Physics was taught in 1950s, 60s, 80s, 80s, then all on keyboard now.

[michaeldamolsen]

Every time I watch one of your videos I am struck by the extreme quality of your explanations and your ability to make the material accessible to those of us without a long formal education. Thank you for all the time and efforts that have gone into producing these videos!

[NoName-qvzm]

Man, you should be given a Nobel prize for putting this all together. Very good explanation!

[hughmungous]

Watching your content is like watching a new lemmino video for me; an absolute treat!

[IntiNikelaos]

As a physics major drop-out (I dropped out because of many things, some beyond my control, but one was that I had communication issues with most professors), I’ve never seen such beautiful and rigorous explanations for both such simple concepts and different areas of knowledge as what the standard deviation is and how the quantization of energy is related to the form of the wave function (that meaning, how the oscillating nature of trigonometric functions leads to discrete equidistant answers when solving trigonometric equations which leads to the energy states when solving the wave function. Literally, mind blowing!)

[JG-zstr]

For unexpected reasons I’ve been confined to a hospital bed for the last few days. This video was a ray of sunshine, distracting me with an hour of exciting, challenging material. You’ve earned yourself a new patron. 👍🏼

[jeroenritmeester]

I particularly love 33:10 where, without even applying the equation to the real world, the math just collapses into giving such a clean an interpretable result for K. Blew my mind.

[jamesgalante]

Bro. Wtf I love you. This was the best explanation of ANYTHING I've ever seen. It's so freaking intuitive I'm actually flabbergasted. Without a doubt, the world is a better place because of people like you. There's so many videos on YouTube about the Schrödinger equation and quantum mechanics in general. I've watched so many, and none of them capture it like you do in this video. Truly, you are the best teacher I've ever watched on YouTube--and I've watched an unhealthy amount of educational YouTube videos. Like Walter Lewin level. BUT BETTER. Omg I can go on and on. Never understood differential equations or partial differential equations before... now I feel like I can approach those topics by myself. You literally explained why quantum mechanics can be ignored in classical systems because they have large amounts of energy, which make the probability distribution indistinguishable with our instruments. And you did this as an aside. Like I'm halfway through the video and so excited to keep watching. Kudos dude.

[firstolasto]

Today’s generation is so lucky to have these types of videos. Your step-by-step methodical derivation answers so many questions for students just starting out…, I just wanna say thanks. Absolutely brilliant. Definitely the best video on the topic by far.

[JC-zwvs]

A masterpiece of outreach science work There has clearly been so much work gone into this, on every level:- academic, planning, scripting, visual representation and presentatuon. Simply superb. Thank you. Thank you. Thank you!