3:36 "The difference in mass between a proton and an electron is the difference between an elephant and 1836 elephant" Thanks for this insightful comparison

Really like the approachability that you deliver the concepts while also not shying away from the math. I think there's a gap in the physics education space these videos fill.

We're going to be great friends. The low key elephant humor, the quick explanation of every symbol used, not shying away from reality or confusion. This is a great explanation and I will watch the sequels as soon as they drop.

"Have you ever tried to catch a quantum particle?" Yes, every time a photon hits my retinas.

It's funny how I am in 9th Grade, don't even understand anything,but still find this satisfying.I am even watching this for entertainment😂

Just a couple of points about your video, since you asked for suggestions: (1) The 1s to 2s transition is a forbidden transition, so it requires two photons to have it work, not one as you illustrate (1s to 2p is fine and 2p lives in the excited state about a billion times less long). This plays an important role in the Lamb shift experiment and in the proton charge radius experiment. (2) You seem to be using an ontic viewpoint of the wavefunctions, as if the electron is the wavefunction. Some people do use this picture, but it can have a lot of issues with interpretations of quantum phenomena. It might be useful to explain these issues. (3) I am not sure if this is your first discussion of kinetic energy as a Laplacian, but because for waves on a string, the second spatial derivative is the potential energy, some additional discussion of why it changes for quantum mechanics might be helpful to your audience.

Hi everyone, thanks for checking out this video! :) Please let me know if you have any questions or suggestions. I'm still cooking up parts 2 and 3, so I'm hoping to modify those based on your feedback. Edit: lots of great responses so far, thanks everyone! A few of you pointed out that the transitions between 100, 200, and 210 are more complicated than I’ve shown here, and you’re totally right, when thinking about angular momentum and such there’s more nuance involved than just shooting any old photon at the atom. We’ll talk more about that in the next video :)

man, even though there are so many mathematical concepts that I don't understand, somehow I managed to intuitively understand each step to get to the final product, you left me breathless. Freaking amazing!!!

Absolutely wonderful. The KZfaq algorithm is timely in its recommendation of this video to me.

Beautiful presentation ! You not only have a deep understanding of the subject but also know how to make it accessible. Congratulations.

I love that real reason you switched to mu is because you want to use "m" later to mean something else! Honesty/self-awareness is the soul of analysis. Keep it up. Some days the biggest frustration of mathematics is running out of, and keeping track of symbols.

Really glad I found your channel, love to hear the enthusiasm in your voice! I feel the same way about physics, very late to the show, but I'm kind of hooked now. There's always a little Eureka moment when I try to extrapolate on what I'm learning and then have it confirmed or fail, which leads to more learning. Something very Promethean about it, music synthesis really gave me a lot of insight into wave forms, helps visualize the math and make it fractionally less daunting!

Your videos are just amazing! ❤And you radiate such positive energy in your explanations, it's a pleasure to listen. Can't wait for part 2 and 3.

Your delivery is so listenable and you sound like you are having fun explaining this to us. Easy to be motivated with your instructor is enthusiastic. I hope you continue to make more content. It is of great value to anyone looking to better understand bed-rock reality.

This is perfection. After having finished my first quantum course (working up to the hydrogen atom), I found some of the later material as explained in the Griffith’s book to not be so intuitive (especially on 3D wave functions). So this is a really nice bridge between intuitive clarity and rigor, as others have mentioned. Thank you for the awesome content!

This video is fire! I think it's one of the best resources out there for learning and understanding quantum physics. In my opinion, there are three main aspects to learning: knowledge, understanding, and motivation. We know that 2 + 2 is four, but unless we understand how addition works, we won't be able to solve 2 + 2 + 2 on our own. And without motivation, learning becomes challenging. I particularly enjoyed the beginning of this video. The excellent animation made me contemplate how atoms truly behave and why. It sparked my curiosity and motivated me to learn more. Your video has fantastic visuals that help us grasp the concepts, and your explanations are well-timed, clarifying everything effectively. I liked everything about this video, but I do feel that its length wasn't sufficient. However, it's great that you made it that long, as it doesn't intimidate viewers. It also provides breaks and leaves us eagerly anticipating part two. What I would suggest is creating separate videos. I would love to learn more about how quantum physics developed since it's complete beginning. How did Schrödinger derive his equation? Why do we use Hamiltonians? It would be wonderful to see examples of their use. For instance, pose a simple question and provide a solution using the Hamiltonian.

This is so much more clear than anything on this subject I've ever seen!

Very clear and intuitive exposition. His presentation reflects a very clear understanding.

Awesome video! I appreciate your effort to communicate this knowledge. I can't wait to see parts 2 and 3. I have no suggestions. This is just perfectly illustrated to me. Thank you.

😂😂😂😂 the elephant analogy

You did an incredible job explaining it. Thank you for helping the world’s future students. I read my textbooks for QM front to back many times, and this video was the first I’ve seen to teach by intuition instead of ”hope you learned linear algebra and statistics”

I am actually impressed and excited by the way you are explaining things. Just excitedd for the next parts!

one of the best videos I've seen in a while

Absolutely marvelous! Really looking forward not only the next episode, but every new video of yours! Keep it up!

This is such a well made video. Gonna watch every part that comes out

Strong work here. Great visual aids and a down to earth approach focusing on the concepts but not ignoring the mathematical rigor. I subbed and expect your channel to grow appreciably over the next year. Congratulations.

This is an incredible explanation that doesn't shy away from the complexity. You sir have gained a subscriber.

Loved It! Can't wait for the next part. . This was done really well!!! Thank you .

We covered some of this in my intro to materials class, but it is really nice to have much more detail, thank you

Great video! I can't wait for part 2 & 3 🙂

"let's solve it for PSY, how hard can it be?" - To be continued Perfect cut x) Good video thx

Loved It! Can't wait for the next part. 🙌

ive been looking for something like this. Perfect. Thank you.

I don't understand 85% of what you're saying but every day I wake up in a world, astonished that a collection of probabilites has collapsed into a chair, a tree, my dog, my child. I'm amazed that humanity can go about its business knowing what lies underneath. I think it should be mandatory that everyone stop at least once a day and consider how incredible it all is.

That's like comparing the mass of an elephant and the mass of 1836 elephants LOL!

Lovely in every aspect!

These are awesome, I'm still in middle school, so I don't really have access to study things like these, but this is nice, your humour is impeccable and it is also easily followable ;)

Your intuition and explanations are on par with the clarity of Griffiths! Love it ^^

Probably the best video on the Quantum Mechanics of a Hydrogen Atom I have seen so far. The animations are great.

One step closer to actual insight....thanks :) many more to walk

Amazing Video so keen for part 2

Thank you for making such high quality explanations. Your videos are perfect for the curious high schoolers out there that want a glimpse into advanced math and physics :)

Beautifully produced❤

Pure gold! Thank you! Never stop producing such quality videos!

Beautiful. Thanks for putting the spark in it!

this video is beautiful, you made a great explanation, keep doing videos with this quality

Wow. Just wow. I just found this series is amazing! I want to learn the math behind all of those concepts but most videos don’t include it. This one was very good! Thank you!

Amazing, I'll wait for the second and third part. Great work!

Absolutely brilliant, elite quality

Not sure how I ended up here, but I will revisit once I relearn physics.

Great video! Thank you.👍

bro u have earned my sub. The way you explain how it the increasing uncertainty is what causes the electron to remain in discrete orbitals.

This is brilliantly done! Keep them coming. I’d bet you’d crush a video on renormalization.

Your tone is amazing!

Wow! Great explanation!

This is so succinct and starts from such a nice point. Very intuitive (As intuitive as quantum mechanics can be in a KZfaq video). Thank you for this!

That was awesome. The best introduction to quantum mechanics I've ever seen!

Love this video and the approach u use for math, it's simple enough but not trivial

I can't wait for the next part!

Amazing animations. Really needed to see this.

This video has exactly what I was looking for. Thank you.

Many thanks for pointing out that Maxwell's equations break down at the quantum level of a hydrogen atom. I'm embarrassed to say that even after decades I didn't realize this! That was also a very nice explanation of eigenvalues and eigenvectors that you snuck in there. A mesmerizing video in both scope and clarity. Thank you so much!

Holy flip amazing video!

Love the perspective at @3:36.

I’m looking forward to parts 2 & 3.

Woow! Great work dude! Glad I found your channel 👍

Suppperrrr man, bringing down those math symbols meaning to visual level, you make as a fantastic journey...

Very impressive presentation.

Thank goodness. I've been trying to learn this topic and have been repeatedly frustrated by explanations leaving out critical pieces and not explaining why or just doing some hand waving when the math gets hard and they don't feel like explaining. Thank you. I look forward to the future parts of this series.

oh yes. next level education! thank you!

Hey! I recently found your channel and I love it! As a freshman year high school student, I try my best to understand these things and you explain them greatly! I myself have attempted to do something similar to this by graphing out a two dimensional intersection on desmos (my mathematica trial expired). Only it was a different equation for the wavefunction that invoked other things like spherical harmonics and a myriad of polynomial functions. It was ultimately a failure, I think I might have graphed it wrong but I’m uncertain. Anyways, thanks for making this masterpiece! I’ll study it a bit further and try applying this to my project.

Really liked your video! Dont apologize for the maths, it brings the light to the whole thing

I need you to understand how picky I am about science content creators. Particularly on topics like this. You have earned my subscription.

Love the intro man

This was done really well!!! Thank you 🙏🏼

Hello! I liked your video, it could be used as educational material in QM courses at the university xD Very good animations and simple explanations! Can't wait for pt2!!!

Amazing work! As an engineer in Aerospace and (theoretical) mech. Eng. I understood everything! (as far as we can) This evolves my passion in physics and maths! Can you show in one video, how you did all of this visualizations?

Great introduction. Looking forward to watching following videos. I'd like to share one tiny observation I made (only recently) about spherical coordinates that no-one seems to mention, but when you see it, it's one of those 'how could I have missed this?' moments. And that's that phi essentially looks just like a circle with a line of longitude drawn through it, and theta looks like a circle with a line of latitude drawn through it. This must have been why these Greek symbols were originally chosen, but I've never seen this easy aide-memoire written down anywhere.

love this one!

bro u r DA best quantum ytber!!!!!

GREAT VIDEO!!! I watched a few times!

amazing video!

Your knowledge is truly God Gifted 🙏

Wow, really can't wait to come across this on my education!

litteraly can't wait for part 2

This is amazing

Wow! This is amazing work!

Absolutely excellent. I feel like I've been studying this stuff forever, and then someone comes along, like you, that makes it all that much clearer with superb presentation skills. Thank you. I wonder if Theta could be called a declination angle?

Dude, very nice.

The Final Year Project of my BS degree was on scattering cross sections of reactions of important astrophysical reactions. I wish you had uploaded this then. I remember sitting for hours in my lab and trying to get an exact solution to the P.D.E you ended with. I didn't have the math skills. It took me about two months of going on tangents to actually accept that I can't really do this using Laplace's Transform. I went ahead and completed the project but this problem sort of set me on this path of learning higher mathematics. As for suggestions for the next 2 videos, I would want you to slightly hint at confluent hypergeometric functions like say their names because enough people don't know about them and I find them fascinating. And I love all your videos. Things like these keep hearts alive!

Love it! When might we have the pleasure of viewing part 3?!

Cool annihilation sound! Thank you!

I think this is the correct way to teach those you really have to move at kind of a clip, because if you slow down, people will get bogged down in the weird notation and all the symbols and things which are very easy to understand if you just look at the whole picture quickly and then let your brain figure it out, but every difficult if you let your brain get really granular. My professor opens this topic with teaching Dirac notation at the same time so obviously it didn't go super well.

I completely lost it at the elephant - just brilliant

I don't usually write youtube comments, but this is one that I truly feel I owe to you, the creator of some of the most comprehensive and thought provoking study videos in the physics side of KZfaq that I've personally come across. Another reason I don't comment much is because I'm a serious yapper, which I assume anyone who reads this will soon find out, and I doubt anyone has the time or interest to read what will inevitably be at least two or three paragraphs of melodramatic nonsense. If you'd like to skip the context, the last paragraph is really the only one I hope for you to see and recognize. I'm a 26 year old who always had a passion in physics, but grew up constantly telling myself that I'm not cut out to understanding these things. That would mostly stop me from even persuing that passion into something greater. Every now and then, though, I would be inspired. I would be so inspired that nothing else in the world would matter to me. There were times my life would literally be falling apart around me {a bit of an exaggeration, but it's better for the story} and even still, I could only think about solving the problem which inspired me, and that's where all of my energy would go until I was able to come back to some sort of normalcy. I've never gone to school, so I don't have any formal education of anything beyond AP Highschool. This has made it difficult for me to accept my interest in this subject due to some sort of asinine supuriority complex I was projecting onto myself. For a long time, I didn't even think I had a right to be interested in learning something as deep as Harmonic Oscillators, the Schrodinger equation, or other principles/equations that could go as far as being the necessary tools to begin explaining the abstract nature of the vacuum and how it acts as some sort 'medium' (Not aether, although I'm not going to completely rule it out until I can understand the math that tells us it's impossibility) to bring Bosons and Fermions together to form what we know as matter. Or, at least, that's at the core of the question I'm currently trying to disprove for myself. Whether or not I'm successful is inconsequential, as the further I delve into these equations, the closer I come to understanding the nature of the universe. Although, it sometimes feels like every answer puts me 10 steps backward, lol. I'm still a complete novice, but I've accepted the fact that my mind is curious and creative enough to think more deeply about these notions, even if it is currently misguided due to an inexperience with the language that the math forms around physics. I've been subscribed to 3Blue1Brown for years now. I found your channel after watching his Essence of Linear Algebra series, and I have to say, it is likely one of the greatest channels I've come across. You go into the detail. You present it in a way that is entertaining. You show visualizations to help with making the equations more intuitive for those of us who aren't familiar with the mathematics of it all, yet. I haven't actually visited your channel yet, but even the first 5 videos I've watched from you has filled at least 10 pages of my journal with notes either from your direct lectures, or from the subsequent research that your lecture spun me into. Last night it was the harmonic oscillator, which I then spent 4 hours researching and studying. Today.... It will likely be the same because there's a lot that goes into that. The point is, though, that I hope you are able to recognize the inspiration your videos provide to others, and that you are genuinely the 3Blue1Brown of physics youtube. I don't like comparing people to each other, especially in this manner, but I mean that in the most complimentary way possible. You're amazing at what you do with these, and I sincerely hope that you keep making this content. Or, at the very least, that you walk away knowing that you made a hugely positive impact on at least one person's journey through this never ending whirlpool of theory and calculations. I've only just begun watching your videos, and I can already say that you've made that impact on at least me. Cheers 🍻

Wow nice, great video, even though im not at this level yet, i can follow what is going on (sort of haha), subscribed.

I don't care what people think but acc to me you have potential to win Nobel prize in future

Really love this Richard! I barely understand anything here, but I want to go deeper and grasp it properly. Keep doing this, I hope to see the other two parts in the serries! The presentation and the way you explain this is captivating and very easy to follow, that is before all the math creeps in and starts crowding the place. If I would ask a quiestion, it would be when you define the wave function ... is it a quaternion? Is this why it belongs to the complex numbers? Or is the time component considered an imaginary part? Does it evolve back in time? Or is it that the spherical coordinate components are each imaginary numbers like in a quaternion (like i, j, k)? I see in previous slide (@5.35) there is a complex phase, but a phase supposes two waves that need to be in or out of phase by a certain time maybe? So I guess the time is the Complex value in the wave function then? If you could expand on this, it would be great!

Great explanation and amazing visuals. Keep up the great work I really struggled in pchem 2 and this really makes me happy to understand it better again.

Really great approach to explaining quantum physics. I really wish all electrons made a little cartoon “PLOP” sound when they changed states. The world would be a cooler place.