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Wow... Amazing 🤩

The Steam engine has done more for science than science has done for the steam engine😃

Sander, you are amazing for putting time and effort into producing and publishing these videos. You deserve so much more views, this is just simply breathtaking.

Imaging single atoms with high NA optics is an important part of what I do, and this presentation pushed my geometric intuition for aberrations over a long-standing mental hurdle. Subscribed and watching lots of your other videos soon. Thank you very much!

12:05 YDS exp.

Please slow down!! you are not giving enough time for the viewer to register what you just said. Go slower please!!

Superb teaching. Thank you, Sander Konijnenberg!

Great work!

Crazy that this is the first time I'm seeing this. Great video!

Just one more comment about your very nice video. You might find using a projection operator onto even and odd combinations of the upper and lower spinors and focusing on the even sector, allows you to map back to the Klein-Gordon equation. This can potentially get you to the final answer faster than the way you are using. This is covered in Glauber and Mqrtin’s papers in the mid 50s and is describe by Baym in his book.

You have to be very careful with applying Feynman-Hellman to the 1/r^2 expectation value. This is because in the standard solution, l is an integer. You have to first show that the results do not require l to be an integer, find the energy eigenvalues for arbitrary l values, which actually breaks much of the degeneracy of the hydrogen energy levels, take the derivative, and then take the limit where you real parameter is made an integer. The final result is indeed the same as what you derived, but just taking the derivative of an integer is not really valid. It can also be derived using operator methods without Feynman Hellman, but that is a bit involved. The Kramers Pasternak relations can also be calculated using operator methods. The expectation value for 1/r^3 is not well defined for l=0 and cannot be used for that case. The Darwin term corrects this issue and gives the same answer you would get by ignoring this issue. I assume you know this, given how much you look into the history, but it was not mentioned. I see you do discuss this later.

When introducing the fine structure constant at 16:23 there is a typo, in that you state that the value is approximately 0.07... instead of 0.007...

What is the argument on why an unabberated system corresponds to a spherical wavefront? I get that the argument here is that in an unabberated system, the rays converge to a single point, and the only shape which is perpendicular to those rays thus has to be a circle (or a spheric surface). Can't there be a non spherical wavefront resulting in a diffraction limited spot size? And why (not)?

What is the definition of the term "pupil" here, and what is the pupil in an exemplary imaging system, e. g. a camera lens? Is there a rigorous definition of what you mean by pupil or the pupil plane in the context of this video? Maybe it is also a language problem, I am German and did not find a fitting literal translation.

Great tutorials! Thank you!

Can I get more information about 39:10? Why can spectral line's intensity and frequency of light be written as Ae^iwt? Also why does adding all these Ae^iwt lead to describing motion of single electron? Can I also get explanation on why multiplying two electron's motion is important? I understand that this allows us to find x1(t)*x2(t) with only knowledge of x1(t) and x2(t) but I don't see why this is important.

Fantastic. Thank you for this.

comprehensive, historical, detailed. thank you

The longer someone needs to explain something, the worse is the explanation.

This is the best explanation of telecentricity I have ever heard!

Superb work of excellence.

Very concise, clear and precise! I hope you are doing well.

Nice video. Thanks a lot

I don't think that non-determinism is necessary for free will. In fact, I would argue quite the opposite. When you exercise your free will not to murder someone, you're not just acting randomly -- you're (hopefully) thinking about what the consequences would be and acting accordingly. That kind of logical reasoning requires determinism at some level. To the extent that reasoning is being done in your brain, it's happening despite any underlying randomness, not because of it. We do have the feeling that we are able to act randomly when we want to, but I think that's just a subjective feeling, and it tells us nothing about whether physics is fundamentally random or not. We have that feeling because we don't have full access to the state of our own brain, and are therefore unable to fully predict what we will think in the future. Just as we wouldn't be able to predict the weather more than a few days ahead, even if all the underlying physics were completely deterministic. So it seems to me that the issue of free will and the issue of whether physics is fundamentally deterministic have nothing to do with each other, and attempting to connect them won't lead anywhere useful.

Thes are the best intro courses, because if you have a math background, you can really enjoy the modeling and power of applied math. Thank you so much!

Tak!!

Grabbed my pen, notebook and completed half this lecture....I am just amazed to see and learn those interconnection....thank you very much❤

Everyone better watch this video in 0.75 playback speed. He talks so fast

🫷👁👄👁🫸 🦵 🦶 how my brain sees me after realizing that other brains be out here like :

Please bring back your Taylor Swift cover 😢

As I am revisiting these material, sometimes I am bit frustrated as to what details can be omitted, and what details are critical. For example, the Haidinger fringes, if two extended sources are separated by delta_z, then, using the same lens, they should not converge to the same point on the screen, but slightly offset due to delta_z, correct? is that because the extended source is very large compared to delta_z, so the offset is negligible? Then, when you show theta \approx r/f, isn't here r needs to be small compared to f for the approximation to be valid? I find it difficult to see how this approximation is making sense here, as the ring pattern is observed at a scale much larger than f. Then, at thin film interference, isn't that the derivation using wave formula assume the screen/lens to be horizontal, as the comparison is done at two refraction points rather than the two points on a line perpendicular to two rays, like the derivation using geometry? In addition, only the phase accumulation from z direction is counted for the ray travels in medium, but not accumulation in x direction, when the ray travels 2dtan(theta_2)? I tried to find answer to these questions in books and on internet, but no one seems to bother to mention. Hopefully someone can answer these questions, I fully understand that my understanding may be limited and my questions may be silly.

A hologram is not actually 2D. It is a 3D object with thickness which is required to create the hologram. Why is this not mentioned in any videos I can find on the subject?

Science instruction does not get better than this. I feel like I struck gold finding this channel. Superlatives do not even give justice to the crystal clear explanations that you give. Many thanks!

I think at 18:41, you shoud write the extra ∆P∆V which would then approximate to 0 when taking ∆P and ∆V as dP and dV.

I've watched like 20 videos on this topic, and this is the first time I understand the concept fully, and in under a minute, great stuff!

Excellent, and very much in the spirit of Griffiths or (the late mathematician) Harold Edwards. Was there an earlier version? I recall watching this more than a year ago. Really inspiring work!

At 11:59 ish where you show the field at z_0 is 1) fourier transform of original field 2) times exp(i*k_z*z_0), 3) then take the inverse fourier transform. I was a bit confused what does "fourier transform of original field times exp(i*k_z*z_0)" mean, semantically. for example, what does "propagate each plane wave to plane z_0" really mean, or what does propagation really mean? it is described as if propagating a field is obvious using the field's FT and exp(i*k_z*z). After searching a bit, I found a potentially better explanation should be if you plug in u(x, y, z) in its iFT expression of u_hat(fx, fy, z) into Helmholtz equation, you get a general solution of u_hat(fx, fy, z)=u_hat(fx, fy, 0)*exp(i*k_z*z), then you take the iFT to get u(x, y, z). Overall, very good presentation, truly allows me to think deeper about the subject that I wasn't paying attention to when taking the course at University.

I really enjoyed this video! It was a real delight to listen to the history of Physics and gain a deeper understanding of how the laws of physics were ascertained

Perfect. One comment about so-called the "collapse of Schrodinger function". Such talk@vocabulary is...poetry or psychologizing. The wave function exists in an "artificial-mathematical" phase space (as a complex plane). Still, it does predict the outcomes of experiments not with a "particle" but only with a stream (set, bunch) of them - by an analogy: a probabilistic formula predicts the outcome of every lottery: does it mean that Loterry machine "collapses" the probabilistic formula to get winning numbers? A nonsense talk!

@ 10:26 According to Hyperphysics (or better, the Department of Physics and Astronomy at Georgia State University) heat is the transfer of energy (like this: 23:07). Hanging on to this widely accepted definition, concepts like heat flow and heat energy tend to confuse people. It may even lead to a similar error like this: dU = dQ + dW. This is wrong because Q and W are already defined in terms of a change in energy. Thus, it should be: dU = Q + W. @ 13:27 Just switch the i and s irreversibly. @ 44:48 Nowadays, particle physicists want us to believe they can track the traces left by the unobservable Higgs boson. @ 47:54 And I like to add this advice: always be skeptical about what your read and hear in TH-cam-videos too. Simply accepting what you read and hear isn't very scientific.

Your channel is an absolute gem and criminally underrated. You clearly are a gifted educator and scientist. Wishing you millions of views and subs.

55:43 - - the soundwave of a certain b*tch. I know about them b*itches. Man your work is phenomenal, it's like a year's course in 2 hours.

OK not completely: at 17:50nn-the typical textbook nonsense on "time dilation". In the "Moving" system (x',t') these parameters x',t' represents not the values "recorded" by the moving "mythical observer=the set of synchronized clocks) but the ones as "been seen" by the observer in the system at rest! The "moving" observer records the same values of x',t' as the stationary observer,i.e., x,t; otherwise, it would violate the 1st Relativity Principle, then also that the unit time (of a clock) and distance (of a "rigid rod") is not "on2=1 sec,ore else)! Consequently, the case of "muon" (as a clock) is the same textbooks BS: a "muon" is a statistical "being=wave packet"; hence, all these experimental data can only be explained if one treats this "muon" as a "wave"; otherwise, the 1/3 of experiments data cannot be counted for -see the diagram for both radioactive "objects" at rest and "moving": in t>T(1/2-a halftime) the values of both functions are almost the same even graphically! One a better exposition of the Subject but not completely again

This is great! I tried to understand Heisenberg's magical paper for so long. This really helps! =)) THANK YOU SO MUCH, SIR

That was 🎉

I am totally in love with your work and content on youtube. You are providing something that many books fail to deliver, developing the subject in a chronological order. I just wanted to ask you that, will you be covering relativistic quantum mechanics and dirac equation anytime soon in future? eagerly waiting for your upcoming videos.

You have done great service to the small community of Physics Students who wonder How & where from was so much Linear Algebra & Operator theory was forced upon humanity in the Historical development, esp when we study QMech in the Modern way from J J Sakurai and the like... Thx a tonne!

Your work explaining the historical development of quantum mechanical models if fantastic and greatly appreciated. Thank you!

This answers so many questions I had about the transition from old quantum mechanics to current QM for so long!

Thx