The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics

[@OLApplin]

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

[@youssefsaidi7873]

Actually it's not the difference , it's the ratio , but whatever

[@hagen1555]

I laughed too hard at this :D

[@spencerwenzel7381]

I just had to look at my 1836 elephants in my backyard and this made so much sense

[@paulg444]

take two: "The difference in mass between a proton and an electron is the difference between an elephant and a relatively small cat "

[@Manuel_Bache]

​@@spencerwenzel7381You did by looking at them, but I did by weighin them!😂😂

[@johnsjarboe]

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.

[@splat752]

I think there is a gap between the math and an accurate description of reality. To me math is only helpful so much in so much as it sheds light on the underlying processes which is woefully lacking in QM videos

[@angelmendez-rivera351]

@@splat752 Your comment insinuates the mathematics do not describe the reality of the world, which is just a false conclusion.

[@Manuel_Bache]

​@@angelmendez-rivera351Is it?🤔🤔

[@angelmendez-rivera351]

@@Manuel_Bache Yes.

[@JackAndTheBeanstalkr]

@@angelmendez-rivera351 he doth not insinuate, he accuseth

[@SoujanyaGanguly]

This is not a video. This is an art. It was perfect, perfect down to every last minute detail.

[@RichBehiel]

Thanks for the kind words, and I’m glad you enjoyed the video! :)

[@SoujanyaGanguly]

@@RichBehiel Kudos to you brother. Loved the elephant joke tbh😂

[@32rq]

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.

[@lowruna]

I expected him to compare the elephant with something incredible small... I feel insulted on a large scale here

[@AA-dj1vz]

​@@lowrunamass of Asian elephant 4000 kg 1837 smaller around 2.1 kg

[@haakoflo]

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

[@RichBehiel]

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 :)

[@motor9908]

The approach taken for the visual was astounding, since i was a wee-lad always imagining the theater of particles and waves governing the sub-atomic world that resounds the beauty of just our universe. Thank you greatly in short cause this needs more recognition 😊

[@MultiversalGoat]

Can't believe how underrated you are even months after your first few videos! I am lucky to be one of the first few thousands before the millions flood in. I am an electrical enginnering student deeply interested in the big why questions and these last two videos have been legendary for conceptualization. Thank you so much and there's no doubt in mind that your channel is about to reach millions of subscribers.

[@RichBehiel]

Thanks for the kind comment! :) I’m glad you’ve enjoyed the videos, and looking forward to making many more. It would be cool if lots of people watch these, but honestly 12k subscribers is already way more than I was expecting 😅 But it’s interesting to think about the possibilities if the channel keeps growing.

[@blaxbrian6877]

awesome

[@kaMus09]

Here is a question. Why you don't have thousands likes and more? I really cant understand...

[@CHp-up9tx]

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!!!

[@michaelblankenau6598]

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

[@RichBehiel]

Thanks, I’m glad you enjoyed it! :)

[@vtrandal]

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

[@quantum4everyone]

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.

[@RichBehiel]

Great suggestions, thanks! :) I’ll definitely address the transition thing in the next video. The latter two points are very true too, although I might hold off on those until a Q&A video following part 3.

[@quantum4everyone]

@@RichBehiel ok. Good to hear this.

[@NWRefund]

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

[@RichBehiel]

Thanks, that means a lot :) I hope to never let you down!

[@akf2000]

😂😂😂😂 the elephant analogy

[@treybell40501]

It actually made me lol. I thought he was gonna say mice or planets.

[@fidelogos7098]

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.

[@RichBehiel]

I agree! :)

[@lepidoptera9337]

There are no probabilities in your classical world, at least none that stem from the quantum level. The probabilities in the math come from our experimental setup, which is the only way with which we know how to approach quantum mechanics foundationally: by measuring frequentist approximations of a quantum mechanical ensemble, i.e. an infinite repetition of the same experiment. Your dog exists exactly once. It's NOT a repetitive experiment. How reality emerges from "non-repeat" interactions was first explored around the end of the 1920s by Heisenberg and then by Mott (1929). It's caused by continuous weak measurement on the same system, which leads to fundamentally different results than the single quantum measurement picture that you have heard about. The dominant effects in single quantum interactions are angular momentum quantization, relativity and statistical independence. What causes classical physics to emerge from a quantum system are correlations between repeat measurements that are based on conditional probabilities.

[@fidelogos7098]

@@lepidoptera9337 Thank goodness! Now I can sleep at night. I was worried the moon might disappear if we all stopped looking at it.

[@lepidoptera9337]

@@fidelogos7098 It wasn't meant for you. It was meant for @RichBehiel. :-)

[@thecaribbeanbookworm5066]

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!

[@Generalist18]

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😂

[@exo-580]

wow ,you will become super hero!!

[@Verrisin]

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

[@mayonakao2488]

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”

[@benjamin_markus]

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

[@logaandm]

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.

[@jamesbentonticer4706]

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.

[@turel528]

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.

[@Oms-xk2zb]

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

[@RichBehiel]

Thanks for the kind comment! :) I just hope I can get to the frontier of fundamental physics, to see with my own eyes what the fuss is all about. That should be doable, since all the answers we have so far are written in books. Whether I could then make a contribution to push the frontier forward, well that seems like a much harder thing to do! 😅

[@mus3equal]

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!

[@kgblankinship]

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

[@asaliphon351]

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 ;)

[@michaelcharlesthearchangel]

Very impressive presentation.

[@RichBehiel]

Thanks! :)

[@alexkonopatski429]

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!

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :)

[@charleschidsey2831]

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.

[@RichBehiel]

Thanks Charles! :)

[@aanchaallllllll]

0:14: ✨ The video discusses the hydrogen atom in different energy states and the behavior of the electron when photons are shot at it. 4:28: 🌐 The problem has spherical symmetry, so spherical coordinates are used. 7:51: 📚 The energy operator in quantum mechanics is taken as a principle and can be further explored in the book 'Quantum Mechanics and Path Integrals' by Feynman and Hibbs. 11:23: 📚 The wave function allows us to relate momentum and space-time and derive the governing equations. 14:52: 💡 The energy of an electron in a hydrogen atom is a balance between the electrostatic potential and the quantum mechanical fuzziness. Recap by Tammy AI

[@theNERDYwhiteBOYS]

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 KZbin 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 🍻

[@jirisykora9926]

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

[@RichBehiel]

Thanks! :)

[@garyscott4094]

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!

[@RichBehiel]

Thanks for the kind comment! :)

[@RickyC0626]

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

[@VMgeschwader4117]

You will have to revisit maths and chemistry too.

[@kylewhite5695]

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

[@v_munu]

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

[@RichBehiel]

Griffiths is a role model, so that means a lot! :)

[@eklavyachandwadkar6200]

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

[@sumairahmad9464]

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!

[@JackAndTheBeanstalkr]

"confluent hypergeometric functions" and thus endeth the lesson

[@yashen12345]

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.

[@drmarioguti]

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.

[@benwaterz2122]

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.

[@RichBehiel]

Thanks for the kind comment, and I’m glad you enjoyed the video! :)

[@burnytech]

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

[@RichBehiel]

Thanks Burny, I’m glad you’re enjoying the videos! :)

[@kitstudent4446]

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?

[@RichBehiel]

Thanks, and I’m glad to hear that! :) Someday I’d like to do a video on how to make these videos. It’s harder than it seems though 😅 This hobby grew out of about a decade of programming experience, but to be fair the animation codes are usually not particularly complicated. It just requires a decent amount of experience with Python.

[@BariScienceLab]

THIS IS CRAZY!!

[@RichBehiel]

Hopefully in a good way 😅

[@Solicanz]

Absolutely brilliant, elite quality

[@RichBehiel]

Thanks! :)

[@rock3tcatU233]

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

[@RichBehiel]

Thanks, I’m glad you enjoyed it! :)

[@-justasoul]

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.

[@TheJara123]

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

[@csibesz07]

Uhh this is deep. I'm not even a physicists, but a free time adventurer in the ways humans are able to describe nature.

[@Velereonics]

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.

[@astrokevin92]

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.

[@RichBehiel]

Thanks! :) Yeah I’ve wondered that too actually, hard to imagine those letters were picked coincidentally, but no one ever talks about it. I think subconsciously that’s why I usually like to use phi for the polar angle, since the line is slanted so it feels more like elevation or latitude, while theta feels flatter.

[@bobbyobacon9425]

HOW DO YOU ONLY HAVE 31k SUBS????? SOMEONE GET THIS MAN MORE VIEWS

[@RichBehiel]

It’s funny, 31k is already beyond my wildest expectations 😅 The response to these videos has been so wonderful, not just in terms of numbers but just the positivity and good vibes coming from everyone. I feel very fortunate to be able to talk to people who are also passionate about physics.

[@williamharr7338]

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

[@TioCristian-gc7em]

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

[@destructionman1]

Fyi another great derivation of the Schrödinger equation is shown in the video "What is the Schrödinger Equation?" by the channel Physics Explained. Amazing stuff, thanks for this! Oh how I wish we had these sorts of visuals back in my undergrad days.

[@spitzhorneule]

I completely lost it at the elephant - just brilliant

[@willo7734]

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.

[@cesardelgadillo4139]

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 :)

[@_vansh_W]

Idk how i stumbled upon this masterpiece. Just wanted to say im a 12th grade student who knows nothing about this topic especially. But all these concepts and things make me wonder about the world and i really like to think . I will keep watching the videos even when i dont understand many things cuz I just love these things. Thanks for this fantastic video!

[@lepidoptera9337]

Yes, you stumbled upon a lot of bullshit and you don't know better. ;-)

[@andreandes7485]

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

[@RichBehiel]

I’m glad to hear that! Thanks for watching :)

[@paulholloway7666]

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

[@springdoctor]

Beautiful. Thanks for putting the spark in it!

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :)

[@crzyfuture]

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

[@gaurangkuksal]

(Corrected) I just have a small question anyone can answer. So when he said the time dependent Schrödinger eqn (TDSE) reduces to TISE where we want to calculate the energy eigen kets is because the states are stationary with respect to space so that we can separate the time out and then calculate the derivative which straight away acts on the temporal part leading to the -iE/h leaving the ψ(r,θ,φ) invariant. So we basically get the -iE/h from the time evolution part and we get a constant En which would be the energy eigen values for the kets. Does that apply to all systems? As all systems would have stationary (wrt time) eigen values? Or we cannot take that assumption for all states coz I can’t think of any states where energy eigen value changes with time. I am here for revision as my basics are not clear so if anyone knows the systems with time varying energy eigen values, kindly let me know coz it might be obvious and my brain isn’t braining coz ofc quantum mechanics.

[@RichBehiel]

Great question. That’s correct, the energy eigenvalue of an energy eigenstate doesn’t evolve over time. A system can evolve into a different state, but as long as it’s in a particular energy eigenstate, it’ll have the energy eigenvalue corresponding to that state. Energy eigenstates are roughly analogous to resonant modes, with the energy eigenvalue being related to the frequency of each mode.

[@prabeshbashyal6343]

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

[@dmitrypotter3319]

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!!!

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :)

[@jamesgray3312]

Amazing Video so keen for part 2

[@indiaview9414]

14:41 electron-proton coloumb potential shown e^2/r which is wrong but correct potential is - e/r .potential energy is - eV

[@cordec_]

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.

[@Asterism_Desmos]

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

[@RichBehiel]

Thanks for the kind comment! :)

[@gardensoundrecords3598]

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

[@hernandezdiazjuanpablo9817]

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

[@RichBehiel]

Thanks! :)

[@jackpeterkettley]

Been searching for approachable content to share with my significant other of the beauty, simplicity and elegance of the math of quantum physics but have always struggled, I think this is finally the series.

[@Beerbatter1962]

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?

[@RichBehiel]

Thanks, glad you enjoyed the video! :) Declination angle actually already has a definition in astronomy, which is closely related to the theta angle here, but I believe it starts at 0 at the equator and then has positive and negative values. The theta we’re using in this video is formally called the colatitude angle, but people often call it the polar angle or, or speaking casually someone might say elevation angle or latitude or inclination. In the context of distinguishing between the angle that goes up and down, vs the angle that goes around, any of those words are ok, I think. The most important thing is defining what the degrees are and which way the coordinate goes, for example theta = 0 is the North Pole and 180 is the South Pole.

[@Beerbatter1962]

@RichBehiel Very good. That's a great clarification. Looking forward to part 2.

[@jamesbond-th5bl]

I’m writing this comment at 1:34 minutes of video, This is going to be amazing ❤

[@lethargogpeterson4083]

Love the perspective at @3:36.

[@brockvervilles2559]

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

[@RichBehiel]

Thanks! :) I’m going on a bit of a detour for the next couple videos, covering the basics of relativistic quantum physics, so that when we finally return to hydrogen in part 3, we can view it in the context of the glorious Dirac equation. Originally I had planned on just jumping right into part 3, but while putting together the outline I realized it would be more accessible if I covered some of the prerequisite concepts first.

[@_kantor_]

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

[@hamidrezaakhlaghi2348]

you are the first one dealing with quantum mechanics i didnt pause the video

[@sonarbangla8711]

From the classical world the leap to the quantum world is like a transition from physics to metaphysics, when the act of observation measures its effect on the whole world. Like the imaginary number i can express orthogonality and also permit factorization of all polynomial as real numbers are replaced by complex numbers forming a field, stretched on all sides to infinity. This change from physics to metaphysics enables us to enact QC functions, conjectured by Maldacena to encompass the whole universe and all processes in it, as the universal complexity gives rise to life, consciousness, soul and faith.

[@richard8176]

I’m looking forward to parts 2 & 3.

[@davidkent2804]

Amazing animations. Really needed to see this.

[@RichBehiel]

Thanks, I’m glad you enjoyed the video :)

[@zacharyshifrel9107]

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

[@gonzalocastro4761]

I can't wait for the next part!

[@JohnVKaravitis]

4:20 The angles that you have here is how I've always seen it in my physics classes. textbooks, etc. Mathematicians do it the other way.

[@zeluizsn869]

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

[@2gr_t95]

litteraly can't wait for part 2

[@RichBehiel]

Wait no more, part 2 is up! :)

[@2gr_t95]

@@RichBehiel you should expect a "litteraly can't wait for part 3" comment soon then x,)

[@jezza10181]

Amazing introduction with the hydrogen atom absorbing the photon. Thanks for this video its really great.

[@julianrichards9509]

I love the teaching style here,it is natural and fully explained,perfect balance. When you finish the hydrogen atom,would it be possible to show the connection between hopf fibrations and qubits? i'm so looking forward to it,as the hopf video you dropped is gorgeous. i know there is a connection between hopf fibrations and spin,thats all i know!! Thank you,for wonderful lectures richard

[@RichBehiel]

Thanks! :) Yeah, I’d like to get back to the Hopf fibration and qubits as soon as I can. To be totally honest I might be a bit slow to make videos this summer, due to work and family obligations. I have one video planned for after part 3, but beyond that I think returning to the Hopf fibration would be a good idea.

[@julianrichards9509]

@@RichBehiel Thanx for replying Richard,no worries i understand mate,family obligations should be primary, it comes when it comes!!, I'm browsing through your past lectures,as i've just stumbled onto your website,so there's plenty to keep me occupied.Hope you and family are well.

[@skippyXG]

Great video! Thank you.👍

[@CadenHerman-m3p]

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

[@JFBond-zs8xf]

Nice video, but I think you should have talked a bit about the hydrogen spectral series, and the relationship between spectral lines and and electron energy levels, before jumping into the Schrödinger equation.

[@AbhijitShaw-hh3wk]

Your knowledge is truly God Gifted 🙏

[@lepidoptera9337]

God doesn't hand out knowledge. Knowledge is the result of long hours of hard learning. Try again.

[@ehfik]

oh yes. next level education! thank you!

[@gavinwince]

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

[@shmackydoo]

One major thing I've learned from this video is now I can use "you're denser than a proton" as a really intelligent insult

[@IronAttorney1]

Your QM series is great, thanks very much for these videos! They're much more in depth than most videos I've watched while much easier to follow than a lot of the in depth videos I've tried. I'm curious though, what are the 2 unavailable videos at the end of the QM playlist? What am I missing out on? :)

[@IronAttorney1]

Oh another thing... I'm not sure if you take video requests, but I would love to see a video similar to the hydrogen atom ones solving the Schrondiner equation for two electrons interacting, or an electron and positron interacting

[@RichBehiel]

Thanks, I’m glad you’re enjoying the videos! :) I hadn’t noticed that, but those were two rough draft videos that I had uploaded as unlisted. Apparently I added them to the playlist on accident. Also while I was there just now, I noticed that I forgot to add the Dirac video to the playlist 😅 I think everything should be fixed now.

[@RichBehiel]

@peterburgess9735 sometime after hydrogen part 3, I’d love to do a video on positronium (positron + electron), from a QFT perspective. Calculating decay rates and such.

[@IronAttorney1]

@@RichBehiel Oh awesome! I've got you subbed so I'll keep an eye out. Dirac video I'll check out next

[@moej9343]

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

[@risingredstone5949]

4:05: When the emoji pops up at "So much more massive"😆

[@RichBehiel]

Look up “tungsten cube review” on KZbin to see why I’m so enthusiastic about the density of tungsten 😂

[@risingredstone5949]

@@RichBehiel I see what you mean now. Thanks for leading me to that video

[@armagetronfasttrack9808]

I'm not sure I agree with the math in the thumbnail, specifically with the idea that the time derivative part of the TDSE is the "energy operator". The time derivative is not an "operator" in the same sense that the Hamiltonian is an operator. In particular, a quantum operator (e.g. H) maps a vector to a vector. The time derivative, in this context, maps a vector-valued function to a vector. This has importance beyond nit-picky math definitions. In terms of linear algebra, the Hamiltonian can be represented as a matrix which can act on a vector. The time derivative, on the other hand, does not have a definitional matrix representation because you cannot know the time derivative of a vector by only knowing what the vector is. I could imagine an infinite number of different vector-valued functions with the same vector-value at a particular time in a particular basis. They would all have different time derivatives, thus there is no unique mapping of that vector to some other vector. In contrast, the Hamiltonian (and any other quantum operator) gives a unique mapping of that vector to another vector regardless of the presence or absence of time dependence. So the time derivative is not a quantum operator like H is. In fact, the Hamiltonian is defined as the energy operator, meaning that the eigenvalues of the Hamiltonian are defined to be the energy eigenvalues. To say that the Hamiltonian acting on a vector is equal to the "energy operator" acting on a vector is redundant because H is the energy operator. This definition of H as the energy operator is in stark contrast to what the TDSE is saying. The TDSE is a physical postulate, not a definition, that the vector-valued functions of time that correspond to physical reality are those where the Hamiltonian (energy operator) acting on the function at any particular point in time is equivalent to evaluating i*hbar*d/dt of the vector-valued function at that particular point in time. Similar to how eigenvectors are those vectors which map to the same vector whether multiplied by a matrix or by the scalar eigenvalue (even though matrices are not scalars), physical vector-valued functions are those that map to the same vector whether multiplied by H at a point in time or when performing i*hbar*d/dt (even though the time derivative is not a quantum operator). To summarize, there are plenty of (differentiable) vector-valued functions of time which you can evaluate i*hbar*d/dt of at any point in time, and you can also operator H (the energy operator) on at any point in time. In general, the results of these two evaluations are not the same. The TDSE is saying that the particular vector-valued functions where these results are the same for all time are the possible physical states of reality. Saying that \hat{E} = i*hbar*d/dt is both ignoring the important differences between quantum operators and time derivatives, and it is shoving an important physical postulate into a definition which makes it an uninteresting tautology.

[@RichBehiel]

First off, thank you for the very thorough comment! You’ve given me a lot to think about here, and I’ll have to reflect on this for a while. I think part of this might be a matter of semantics. For example, in conversation I’ve often heard people colloquially use “energy operator” to refer to either i*hbar*d/dt or the Hamiltonian. But when being more formal, usually “energy operator” will refer to i*hbar*d/dt, just like “momentum operator” refers to i*hbar*nabla. Those things go together, because after all they’re two peas in a pod, especially in relativity. Wikipedia also has a page for Energy Operator which is based on E = i*hbar*d/dt, for what it’s worth. So I don’t think I’ve broken any of the usual quantum mechanical rules here. But semantics aside, you raise a great point about the difference in character between H and E. I’ll have to think about this for a while, and would love to read up more on your line of reasoning, either via your comments or a source where I could read more about this. The energy operator can be derived from the De Broglie relation, so it’s definitely something physically fundamental, as is the Hamiltonian, but it’s interesting to think about the ontological status of H and E relative to each other, and the different things the Schrodinger equation might actually mean. Of course, that’s a complicated rabbit hole to go down. But as far as thinking in terms of eigenstates, I’ve always imagined the Hamiltonian as a thing that transforms a wavefunction, with the eigenstates being those uniformly scaled everywhere by the eigenvalue. Then the energy operator just comes in as the thing that relates frequency and energy, at least in the time-independent case. The time-dependent case is more dynamic and confusing, but expanding psi in terms of an eigenstates basis, it seems like the same basic picture holds together. So idk. I guess I’m confused in that I don’t know what’s confusing and what makes sense, if that makes sense.

[@williamolenchenko5772]

Excellent! One minor complaint with notation, however. You use the same symbol psi to represent the function of psi(r, theta, phi) and psi(r,theta,phi) x exp (-iEt/h). Shouldn't a capital psi be used to represent the function of (r, theta, phi, t) ? For example, see 10:19.

[@RichBehiel]

That’s a good point! Capital psi is often used to refer to some more general form of psi, for example as you’ve described, to signify the wavefunction including its time dependence. Personally though, I like to reserve the capital Psi for a sum over states, where each state is a lowercase psi. For example, Psi could be a superposition of energy eigenstates psi. In that context, I think it’s definitely worth using the capital. For just a time-dependent eigenstate, it could go either way, at least from what I’ve seen (since this state Psi is just the “sum” over one energy eigenstate psi). But you’re right to point out that there is a meaningful distinction between psi(x) and psi(x,t).