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I like how the music goes out of tune. As Fields Medal Math Professor Alain Connes explains in his lecture, "Music of Shapes," the truth of reality is noncommutative just as the truth of music is also noncommutative.
For those who are interested in knowing a bit more: The special functions that only gets scaled up or down when the operator is applied is called an eigenfunction of the operator. The amount with which it is multiplied with is called the eigenvalue. These eigenvalues turn out to be the only results that the measurement can yield. (this is hinted at around 1:45, 4:25 and 10:45) It can be shown that you can "decompose" any wavefunction into a sum of these eigenfunctions with fitting coefficients. (12:55) The coefficients tells us how likely it is to observe a given eigenvalue that belongs to the eigenfunction that the coefficient is multiplying. The probability is the coefficient squared, as dictated by the Born rule. The function used in the positionoperator, that is zero everywhere except for one place, is called the dirach delta function (3:40). The reason why it must approach infinity at that one point is bechause it is a principle in quantum mechanics that the integrals of the functions have to be "normalised", which is to say that the integral under the curve has to be exactly 1. As it only has a value at this one point, the function value has to be infinity to achive this integral value (6:55). The reason why we integrate is bechause there are infinitely many of these "poles" representing eigenfunctions, bechause the particle could be anywhere along the axis (remember, we are dealing with position), not just at those discrete locations of the poles shown in the animation. Bechause space is continues, the probability of finding the particle at one very specific location (kind of like a point on the x-axis) is zero, bechause there are infinitely many points even in a infinitesmal distance form it. Therefore, the probability for finding the particle is given for a small interval (between x and x+dx) as seen around (8:30)
I have a question, if you're investigating this wave function in 3d (like it is in real life, right), then how does the imaginary axis come into play? does that mean there's another dimension that the wave function is oscillating that is separate from space or time as we know it? Sorry if that sounds retarded
I just want to say, having seen it in several of your videos, the visualization of complex numbers using a spinning wave function (and not just two orthogonal flat graphs) was a mind-blowing revelation for me in how to properly think about and explain imaginary numbers; I always knew they were involved heavily in rotations and oscillations but just seeing sin/cos as a single continuous spiral along the Re/Im axes was like a light bulb going off in my head.
Funny to note also that this shows why the derivative of the complex exponential is itself, while its projections (cos, sin) requires the derivative operator to be applied 4x to get the same function.
You need start working on providing content and integrating your material in electronic textbooks. I think visualization is going to be groundbreaking in education, especially with VR momentum. For more complex subjects, without visualization most people will likely memorize material rather than understand it. This is what's missing in the education system.
by study physics you mean you had a few courses or...? I mean where i'm from when you study physics you go to a school for physics and mathematics and most of your courses are on the topic of physics
I am not in college, yet I watch videos on mathematics & physics at workplace where I take advantages of the quiet times during trade hours. Everyday, I am learning much on RU-vid, Udemy, Open Library, etc.
These videos are great for those who are visual learners like myself. I found the notation to be difficult to understand when reading my textbook, but now that I can picture what the notations mean I'm finding it easier to understand. Thank you very much!!
This particular illustration make such a perfect match with Leonard Susskind's lecture 8 and 9 from the Quantum Mechanics series that it is almost spooky:-)
Agreed. It's a great combination for someone like me, who likes to think visually as far as possible. It makes the maths in the lectures much easier to understand and remember. I can't get over the generosity of Suskind's lectures, and these animations.
Exemplary videos. Even when topics aren't new they are usually presented in a new, interesting and preferred way. I have gained deeper understandings and new insights from your videos. Thanks.
A brilliant animation. Watching these quantum videos has deepened my understanding immensely. I am a physics graduate but seeing these wave functions and operators illustrated with both their real and imaginary components changing in time has helped me understand all this properly. Also, the way the rate of change of the wave function with respect to space and time relates to momentum and energy was brilliantly demonstrated - the logic behind these operators (inc. the position operator) has now become apparent. A brilliant contribution to physics education. Thank you Eugene.
You showed in this video exactly, what I have been trying to understand and imagine from mathematical formulas at last days, which was really hard. You showed it in a much nicer and easier way. I wish I viewed this video before attempting to understand those phenomenas from math formulas. I think, that learning physics at university would be much easier and enjoyable, if students could watch such videos with animations during the lectures. Then learning hard to understand (at first glance) math, that stand behind physics phenomenas, would not be such repulsive. You are great! Thank you for your videos!
Thankyou for such illustrative videos. The best part about this is rather than drowning us in the mathematical procedures you've demonstrated their physical significance.
Absolutely wonderful! I am currently watching Leonard Susskind's lectures (from the Theoretical Minimum series), and these illustrations are perfect complements. Eugene's beautiful illustrations simply *has* to be watched together with Leonards's mathematical formulas!!!
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The quality of presentation is amazing. I have watched the videos on this channel for many years, and am finally taking a quantum mechanics course this quarter. I am so excited to finally understand the maths behind the intuition, thank you for motivating the material!
Absolutely wonderful! Your graphics enliven the equations. The two together make for a complete "picture" of the quantum operators! Brilliant. (BTW, please do NOT change or omit the outstanding musical selections in your videos; they enhance the experience of learning and make viewing the graphics so pleasant.)
great videos... very useful for visual learners like me... i have faced lot of problems in visualizing mathematics and your videos are helping me a lot. the great thing about your videos is that they contain technical stuff ..most videos with visuals cover only beginner material. thankyou...
I am very satisfied to watch this on youtube. Thank you so much for making these types of video. I understood very little by reading the book but after watching this video Quantum Physics is getting clear for me. Really appreciate your hard work.....
I love your videos so much, especially the ones you first uploaded. I appreciate that there are people who understand, enjoy and benefit from this video but this is too complicated for me even though I try my hardest to understand what is going on. I would love more videos like the ones you uploaded in the past. However I will always remain subscribed as most videos are brilliantly executed and thought provoking.
+aaron morton, thanks. Many more videos similar to my earlier videos are on their way. Though, many people have also been asking me to also cover some of the more complicated topics, such as the one in this video. Therefore, although most of my videos will be similar to my older videos, there will occasionally be a video like this one, which goes more in depth with the mathematics.
Don't worry Sir. Even if I have some trouble understanding all of this, it is nonetheless incredible work you do! Surely a proof that the right teacher can make every Topic enjoyable.
Thanks alot. I find quantum mechanics so hard to understand qualitatively. It is from this video that i understood what a imaginary "i" in sinusoidals actually mean. helped alot
Quantum Operators,magnifica explicación,excelente presentación,brillante la calidad de este video,the music is beautiful,thanks very much,greetings from México.
If the particle is at a known position x=a: the wave function has modulus sqrt (delta (x-a)) where the delta function is the function that is zero everywhere apart from at 0: the integral across the reals is 1
time translation in QM: Schrödinger picture: observables are constant, eigenstates are time evolving, more likely if you consider that Schrödinger picture are analogous to lab frame in SR, Heisenberg picture: observables are time evolving, eigenstates are constant, analogous to comoving frame in SR, hence its eigenstates always at phi(t=0)...
Thank you for making these, and trying to make them accessible to people of all levels of physics education, while satisfying those who have studied the maths. The concepts involved are complex but clearly explained, so I enjoy watching them, trying to learn all of quantum mechanics. (The red and green here make me want gummy worms.)
Really appreciate your clear style of explanation. I am grateful for the new insights that I got from the video. The background music makes me feel so curious.
These videos are crazy good like wtf actually you and the team you work with seriously hit the jackpot in making this stuff as entertaining as it can be super kudos to you and your team unless you do all this yourself then super kudos to you
Just started picking up quantum mechanics in my spare time, and without any prior knowledge (other than calculus to understand some of this more formally) this makes so much sense! Amazing job
Returning a few months later. Everything makes perfect sense now! Thank you again, for inspiring many of us and helping introduce some fairly complicated concepts visually and intuitively.
You must be a genius. This way of explaining operators is amazing. This is the future of education I agree. And I don't agree with people that don't like the music, it is helpful for me, the music is proper in my opinion. Thank you very much! Liked and subscribed!
Nice Job again, Eugene! I would like to see a short video about Dirac's equation and antimatter as to see how can you find negative solution for the energy of an electron or any other particle. I know that in this is video you talked about energy but it would be nice if you could go deeper because I can't find any video that explains it well. Thank you!
Very good videos, your animations are the best in youtube! Thanks for all your contributions to public knowledge! Just my humble opinion: I find the music very distracting sometimes, the tunes are too striking or too loud. They are lovely tunes to pay attention to, not designed for background music EDIT: I just saw a comment you made months ago stating that people watch the music versions more than the once without the music. I'd like to clarify that I only criticized the volume and style of music , not the fact of adding music to the videos. Adding tunes like Turkish march or Fur Elise, which are very recognizable to people may lead them to follow the melody more than the words in the video.
+JRussoC, thanks for the compliment about my videos and my animations. I realize that a lot of people don't like my choice of music, but I don't think that there is any selection that will please everyone. In any case, thanks again for the compliments.
Please make these simulations about quantum physics much precisely and deeply so your videos help us in our study thank you man may you live long !God bless you!good luck
Great graphical illustration of Quantum Operators on Wave Functions. All complexities associated with Quantum Mechanics and Complex Quantum Operators simplified through animations.
Excellent videos! Love how you make such a difficult topic easier to understand. The visualisation is also intuitive for describing the Heisenberg's Uncertainty Principle, where there is a trade-off between momentum and position. Smaller spirals lead to larger d/dx, lead to larger momentum. Wonderful! Perhaps you could explain why the energy function scales the wave function by the same amount? I would think this provides more intuition. I can't explain very well, but I'll try: considering the x-axis as the centre of rotation, and each point of the wave function being on the circumference of a circle, the angular velocities of all points are the same.
It does not. He trying to say he is looking for an orthogonal base (of eigen functions) so that doing linear combinations (i.e. superpositions) representations are possible… I think….
Thanks a million.Your videos help us to clear our concept maths and physics ..I want to request u that please make a video about tangent, normal by its physical meaning and about quantum physics with history.I will be greatful to you forever.
I was interested in quantum mechanics from 6th semester but I could not understand the concept of operators in quantum mechanics when I saw this beautiful simulation about operators ,now I able to understand the base of quantum mechanics much interesting simulations you present thanks
+Physics Videos by Eugene Khutoryansky You help students develop a much deeper understanding then they could of ever gotten from attending a university lecture. You should be very proud of what you are doing here. The intuition behind a concept, in my opinion, is so much more important then being able to compute or prove it. Not to say that the latter isn't important but the main emphasis should be to properly explain the intuitions behind a concept.
so helpful exactly what I am learning in QM 1 this semester. it really helps to see the wave functions in complex's spaces like that. I never thought of the wave function as rotating throw complex's spaces but its so obvious now thank you so much.
From someone who's dabbled in animation. It looks like there is no motion blur being done, which does involve more computations. But without motion blur, there is a resulting stroboscopic effect which is not only distracting, but interferes with the visualization of what is happening. Something worth considering. Also constant stroboscopic effects can be a problem for people with photo-sensitive epilepsy. Not sure in this case. And a question please. To the balls have any significance, or just a result of how the animation is being done?
So basically in 20mins you have just helped me to better understand the first 8 hours of Leonard Susskind's lectures on the mathematical techniques, which I shall now be able to take forward. I can't criticise because these techniques were probably not widely available when LS's lessons were filmed. The younger people are continuing to "build on the shoulders of giants".
I am a huge fan of your work ! i would like to make a somewhat similar series for the french youtube community. could you please tell me how you make all these marvellous animations. which software do you use ? you apparently use a 3d model library, is it included in the soft ? did you get it somewhere else ? thank you for your constant effort, and content delivering. I believe you are going to start a new movement in physics teaching, where all demonstrations are going to be accompagnied by animations of this kind. I speak of you to everyone around me ! keep it up !
O trabalho do professor Eugene Khutoryansky, através destes software de visualização, tem a força e a beleza que me parece muito com o impacto causado pelos impressionistas da geração de Gaugin, Van gogh e outros... Sou muito grato!
Very tense video despite the soothing music. I understood the part where it says "Don't worry, you don't need to understand that". I'm still looking forward to understand the Grover operator;
AMDdizzle is right I'm sure. For the past thirty years, one of the few things I have been getting ambition about is understanding the Shrodinger Equation and now at last I seem to be in with a chance.
This is a great way to see how eigenfunctions really emerge from the operators which are applied. It would be nice to see some examples which give these answers like a particle in a box for energy.
+Brennan Magee, I show the examples, such a particle in a box, and a particle in free space, in my recent video "Quantum Wave Function Visualization." Thanks.
Wow that was the best yet. Easy to understand with highschool physics. Its the part our teachers were afraid of. Your graphics make it all possible. Probably needs a note about reordering operations from i messing up the maths but thats a trap for an advanced topic