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

[@haakoflo]

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

[@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

[@paulholloway7666]

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

[@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😂

[@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...

[@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.

[@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!

[@akf2000]

😂😂😂😂 the elephant analogy

[@treybell40501]

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

[@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😂

[@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.

[@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!!!

[@kgblankinship]

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

[@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!

[@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! :)

[@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! :)

[@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.

[@RickyC0626]

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

[@gammersunity4117]

You will have to revisit maths and chemistry too.

[@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 🍻

[@burnytech]

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

[@RichBehiel]

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

[@springdoctor]

Beautiful. Thanks for putting the spark in it!

[@RichBehiel]

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

[@indiaview9414]

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

[@WildEngineering]

brother i had just started my mouthwash when i got to the elephant part and i nearly spit it all out

[@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.

[@gardensoundrecords3598]

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

[@HunsterMonter]

0:27 ok I'm not even 30 seconds in and I have a minor nitpick. When shooting light at an hydrogen atom, most transitions are induced by light's electric dipole. For this type of transition, l (lowercase L) must change by one, so 1s->2p is permitted but 1s->2s is not. The other types of transition (dipole mag, quadrupole, etc) might permit 1s->2s, but the probability is lower by several orders of magnitude. I know the point was to show different excited states, but what's the point of getting a physics degree if I can't be annoying and nitpicky on the internet.

[@RichBehiel]

As a fellow internet physics nitpicker, I really love this comment. Thank you. You’re totally right, and I’ll keep that in mind for part 2.

[@jippijip101]

Heyyyy! I'm glad I wasn't the only one with this nitpick, and I'm glad I checked to see if anyone else had pointed it out :)

[@RichBehiel]

Yup, I was too vague on the photons and the details of the transitions. Will examine this in more depth in part 2 :)

[@Solicanz]

Absolutely brilliant, elite quality

[@RichBehiel]

Thanks! :)

[@tealdodo904]

I've been looking for something like this for months; all other videos skip the math or the physics

[@_kantor_]

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

[@peterburgess9735]

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? :)

[@peterburgess9735]

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.

[@peterburgess9735]

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

[@lethargogpeterson4083]

Love the perspective at @3:36.

[@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.

[@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.

[@vtrandal]

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

[@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! :)

[@BariScienceLab]

THIS IS CRAZY!!

[@RichBehiel]

Hopefully in a good way 😅

[@LouisEdouardJacques]

1836 elephants! That's more than the elephant population of the DRC! Of course that comparison falls apart when you realized that's it's really hard to get elephants to have opposite charges in this humidity.

[@skippyXG]

Great video! Thank you.👍

[@logician1234]

Could you do a more in depth video on fundamentals of quantum physics? Some operators and formulas presented feel unmotivated or hand-wavy.

[@RichBehiel]

Yeah, great idea! :) I’d love to. Probably after the hydrogen videos. I’d love to derive the energy operator from the De Broglie relation, and show its relation to momentum. Then in that video or a different one, I’d like to show how we can make waves relativistic by transforming energy and momentum in the same way as time and space.

[@samuelcohen2833]

This video is awesome and so informative, helps me explain to my family how AI encryption works in modern vehicle CAN bus systems 😁

[@jamesbond-th5bl]

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

[@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.

[@maurod6180]

GREAT VIDEO!!! I watched a few times!

[@RichBehiel]

Thanks, I’m glad you enjoyed it! :)

[@blazingdragon104]

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.

[@RichBehiel]

Thanks! :) Honestly I struggled too when first learning about the hydrogen atom back in the day. Things didn’t really click for me until I had some more experience with QM and eventually just saw the atom as a kind of 3D harmonic oscillator, well not exactly but kinda. Then it became less of a chemical thing and more of a geometric thing, that felt easier to explore.

[@cademosley4886]

To clarify that, it's harmonic oscillator-like because the electric potential term is attractive and the the kinetic energy term (the gradient or divergence of psi, the Laplacian) acts like it's repulsive, and that bounds the electron position into the geometry of those energy states?

[@RichBehiel]

@@cademosley4886 yeah exactly, there’s that balance of energies, electrostatic pulling in and kinetic energy pushing out when the electron gets too close, with various equilibrium states occurring when things are balanced. So it’s sort of like a 3D cousin of the harmonic oscillator. The hydrogen energy eigenstates can then be thought of as resonant modes, sort of the ways in which a 3D quantum springy thing can vibrate. That’s just a loose metaphor of course, but it’s how I imagine it at least.

[@brandonwillnecker8060]

@@RichBehiel I think it's more than a metaphor because you can consider the effective potential from the electrostatic + the radial contribution from the Laplacian. You can Taylor expand this effective potential at the minimum to get a quadratic approximation. This would give the harmonic oscillator approximation. I like the energy balancing view as well.

[@RichBehiel]

Very true! :)

[@Nyky95]

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

[@adamtalon9776]

2:21 I like how he just casually asks: "have you ever tried to catch a quantum particle?"

[@Verrisin]

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

[@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.

[@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! :)

[@-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.

[@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”

[@vinniepeterss]

love this one!

[@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 ;)

[@afnDavid]

You had me very confused by pronunciation of one word, Laplacian. The way you say it it sounds like what you get when you pull your boot out of the mud.

[@RichBehiel]

That’s a great visual! I totally hear it. When I first heard someone say Laplacian, I was like there’s no way “laploshin” is an actual word 😂 Some people pronounce it “laplahssian”, but I think that’s more of a British thing.

[@DerekKerton]

LOLed at the elephant weight comparison.

[@MualamaAlien]

Man its beyond frustrating to struggle so much with this material when it seems so interesting.

[@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.

[@gaurangkuksal]

@@RichBehiel Understood. Thanks for the reply and the video again, I really have to understand the spherical harmonics for my own curiosity XD. Also, since you’ve starting putting up some field theory stuff as well, I’m now waiting for a bomb drop on a QFT playlist so that I can understand it conceptually after 2 years of studying that, same as QM :p

[@channel32517]

amazing video!

[@YossiSirote]

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

[@RichBehiel]

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

[@JoséRoig-t9o]

3:36 Great analogy 👍

[@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.

[@ChildishBerbino]

1:53 "there is a deep mystery here" - I agree, why can't p3 come out soon enough :(

[@RichBehiel]

I wish I could make these videos faster! 😅 I work on these nights and weekends between work and social things, so I’ve been a bit slow this summer. But I have a video coming up in a few days on why relativity breaks the Schrodinger equation. Then the next video will be on the Klein-Gordon relativistic wave equation, then one on the Dirac equation. And probably one on the electromagnetic four-potential, and how it relates to the Dirac equation via gauge symmetry. That will build up the conceptual tools needed for part 3, which will treat the electron relativistically.

[@ChildishBerbino]

@@RichBehiel Oh my goodness! We're all in for such a treat. Take all the time you need. I'm sure the wait will be well worth it.

[@surendrakverma555]

Very good lecture Sir. Thanks 👍

[@RichBehiel]

Thanks for watching! :)

[@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. :-)

[@cellosean]

"How hard can it be?" Video #2 of 3 is 46 minutes long.

[@OzGoober]

In the quest to find an anolog of scale, you sir are an elephant amongst micro elephants. from 3:39

[@BlackHermit]

Whimsical and clever. I like it. But I did not hit the like button, please forgive me.

[@RichBehiel]

😮

[@BlackHermit]

@@RichBehiel Listen, I am sorry! OK?

[@josebarria3233]

"How hard could it be" Ends up with PTSD

[@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).

[@TioCristian-gc7em]

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

[@TheJara123]

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

[@Am33304]

Well, it may not matter to the narrator of this video production why the reduced Planck constant is what it is, but terming it as known/mysterious is provocative to say the least, in my reading. But if the Constant should turn out to be one or many negative factors smaller than what we use today, there could be issues related to the chaos-and maths concept of SDIC, “sensitive dependence on initial conditions”? Is that not correct? At its actual (minimal) value, “truth” might be said to be found in calculations made from it as a value and as a reality. Physics may be suffering, as many inside and outside it, because of the uncertainty of our various “constants” - particularly because of the radiating of what we refer to sometimes as infinitesimally small differences in size, PARTICULARLY (and maybe drastically) when extended from the tiniest difference to the utter-most (universe sized) reaches of reality. It is not, I think, an academic speculation. In fact when this is considered with Expansion as another kind of Initial Condition, or rather maybe a “Constant Condition”, the variance from current calculations and present speculation (as well as teaching and applications) could well either destroy physics or begin a “new kind of Physics”. Isn’t something like this distinction of basic measurement values something Scientists in 2024 are looking toward, to reset the science and do away with the so-called Crisis in Physics? Because it’s becoming embarrassing to talk about, particularly when society isn’t interested in the subject itself?

[@lepidoptera9337]

Planck's constant is 1 in every rationally chosen system of physical units. We teach that in the first theoretical undergrad physics class. You need to get an education, kid. ;-)

[@iamnotcaptainyt4953]

Just passed High school and here I am studying quantum mechanics already

[@RichBehiel]

That’s great! :)

[@atismoke]

Jokes on you, im watching this video in the womb!

[@barrypickford1443]

Could atoms be little pinched off or knotted spacetime/blackhole like phenomena formed in regular size black holes. Maybe it’s a contributing factor to all the non locality etc of quantum mechanics? Surely in black holes it is non spacial, non time so the centres of all holes are all one “place” same for atom centres. Listen I’m just waffling sci fi stuff at this point. 😊

[@RichBehiel]

That’s what Lord Kelvin thought back in the day. Knots in the ether. I suspect there might be some truth to that general concept, for the subatomic particles. Check out superfluid vacuum models, for example. It’s speculative, but interesting.

[@thedouglasw.lippchannel5546]

Amazing video - thank you kindly. Since you are a Physicist in the highest degree, I would be honored if you would leave your thoughts on CIG Theory (see above link). Maybe you could take CIG Theory to the next level.

[@RichBehiel]

Thanks, glad you enjoyed the video! :) I don’t see your link to CIG theory, and googling it just brought up articles about cigarettes 😅 What does CIG stand for?

[@abirkumarchatterjee1667]

Grateful🎉

[@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

[@ME-dg5np]

Finally something explaining why electrons do not implode into nucleos... But...🎉 Why electrons are attracted by nucleos ?🎉😮

[@fouzz_n]

It is what it is and no one know why it is It is just it is 🙂🤍

[@alexkonopatski429]

Can someone give me some books, lectures which teach Quantum physics from the ground up with all the math, but it still being somewhat understandable and with derivations and not just „here is the formula“ but „that’s how they got to the formula“ and just giving the motivation behind the ideas and how the physicists came up with them? Thanks in advance

[@RichBehiel]

I’d highly recommend the Feynman lectures! :) Not just for quantum stuff but also a great overview of electromagnetism and physics more generally. Feynman has a great way of making the ideas accessible, and talking about their historical development and context. Quantum Mechanics and Path Integrals by Feynman and Hibbs is very good too, more advanced but very good.

[@giansieger8687]

that‘s really interesting, about a year ago i handed in a paper about this to finish my highschool. I derived (with heavy support from textbooks) the analytical solution to the schrödonger-equation for the hydrogen atom where I took an approach just like this wherd I somewhat showed how to derive the laplace transform in spherical coordinates but i can‘t seem to link it here

[@RichBehiel]

Wow, in high school! That’s impressive. Sounds like you’re on the right track to do great things!

[@edmundofernandes552]

Just my two cents: there are quite a lot of non native english speakers watching it. And sometimes we need to get some help from de closed captions and guess what? Following the cc and the material that appears on secreen is kind of crazy. Maybe if you could speak having that in mind, it would be possible to make what is already good to be even better!

[@RichBehiel]

Hi Edmundo, thanks for your comment. I hadn’t thought of this, but you bring up a good point. I’ll look at how the cc appear on the phone and computer screen, then will arrange future videos with that in mind :)

[@wragette]

A square of a complex number is not a real number. Take 1 + i for instance. Squaring it would be 1 + 2i - 1, right?

[@RichBehiel]

Yes, in general squaring a complex number isn’t real. The only exceptions are numbers purely on the real and complex axes. The reason for this is that squaring a complex number squares its magnitudes and doubles its phase angle, and since the real axis has angles 0 and 180 for + and - respectively, the only angles that double to 0 and 180 (mod 360) are 0, 90, 180, and 270. In the case of 1 + i, you’re right, it’s 2i. You can think of this geometrically too. 1 + i is a 45 degree angle above the real axis, with length sqrt(2) from the origin. So when you square it, it’s 90 degrees from real, and has length 2. So it’s 2i.

[@howardlandman6121]

You can't get from the spin-0 1,0,0 state to the spin-0 2,0,0 state by absorbing one spin-1 photon. It violates conservation of spin.

[@RichBehiel]

You’re right. I was too cavalier with glossing over the details of transitions between states. My intention was just to make visual the idea of photons popping the electron up, then it falling down and emitting a photon, but I should have been more careful to show only realistic transitions between states.

[@akshatjain2775]

This is art.

[@kylewhite5695]

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

[@TomTalley]

Stumbled around trying to understand this topic and finally found you by coincidence of search terms. I have a link to a conversation I had on the topic I would like to share with you to gain your opinion. Would it be ok to post it here. I keep thinking that this stuff is all RF. Harmonics and phase relating to spin and stuff. The math is beyond me, but as an RF guy, I can see the shapes and understand orbitals as vibrating elipses of length defined by energy and frequency defined via h....is that about right?

[@haukur1]

I think the phrasing of your introduction to the uncertainty principle is a bit off. It's not that the more you know about the position of the hydrogen the less you know about its momentum. It's that the less the momentum is _unknowable_ or inherently undefined. In other words, the uncertainty principle is a bit of a misnomer, it is not a question of epistemic uncertainty or knowledge.

[@RichBehiel]

That’s probably correct! Most physicists would agree that the uncertainty is more ontological, less epistemic. But personally I can’t rule out pilot wave models confidently enough to say it’s purely ontological.

[@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.

[@AnarchoAmericium]

Then why does the electron interact with a positron to produce a photon? Or sometimes interact (via the weak force) with a proton to produce a neutron (which will beta-decay back to an electron and proton)?

[@RichBehiel]

Great questions! I hope to answer those questions in future videos. The answers are very complicated though. In part 3 of hydrogen, we’ll see the Dirac equation. Someday that could lead to a video on positronium and the two-body Dirac equation, but that’s all very tough to animate. Anyway, electrons and protons can annihilate because they seem to be exactly the same, except for charge. They kind of unwind each other, or at least that’s how I imagine it. The nuclear forces hurt my brain, so I don’t think about those as much 😅 U(1) is hard enough for me.

[@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! :)

[@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.

[@ericstorm4613]

Oh explained like that it's kinda simple!

[@williamredmond8128]

Dude, very nice.

[@kseriousr]

If proton is 30 trillion times denser than tungsten, what's its schwarzschild radius?

[@RichBehiel]

Great question! :) 2.48x10^-54 meters, which is 35 orders of magnitude smaller than the proton radius. The counterintuitive thing about the Schwarzschild radius is that it scales linearly with mass, whereas we’re used to objects scaling with the cube of mass. So it’s easier to make black holes out of bigger things. Imagine making something 8 times more massive, keeping it proportional. Then all its dimensions are only doubled, but its Schwarzschild radius becomes 8 times larger.

[@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.

[@user-qb8fp8oj1p]

Nature😍Science 😘

[@moej9343]

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