Quantum Operators

Quantum Operators for measurements of Energy, Position, and Momentum in Quantum Physics. My Patreon page is at / eugenek

[@EugeneKhutoryansky]

To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available). --To change subtitle appearance: Scroll to the top of the language selection window and click "options." In the options window you can, for example, choose a different font color and background color, and set the "background opacity" to 100% to help make the subtitles more readable. --To turn the subtitles "on" or "off" altogether: Click the "CC" button under the video. --If you believe that the translation in the subtitles can be improved, please send me an email.

[@khachaturmaghakyan3980]

I didn't see the x axes. Where it?

[@voidisyinyangvoidisyinyang885]

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.

[@lsandqvist]

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)

[@lsandqvist]

+Nat King Coules You are very welcome :-)

[@dineshmohanty4726]

Thanks a lot

[@meowmix6401]

fam lmao

[@richb2752]

lsandqvist Thank you very much...You are very smart.

[@tripp8833]

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

[@KutuluMike]

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.

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@jaimelima2420]

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.

[@Akyla0177]

I studied physics in college and didn't undersatnd what was going on. I still don't, but watching this video makes me feel smart!

[@urosgrandovec3409]

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

[@pinklady7184]

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 KZbin, Udemy, Open Library, etc.

[@charbeleid193]

If you have a bachelor in physics and don't understand this it's just sad

[@NafazaGR]

I'm so glad you exist and make these videos. Thank you.

[@EugeneKhutoryansky]

+BlazedHatZarp, I am glad you like my videos. Thanks.

[@chandrakantasarkar7556]

@@EugeneKhutoryansky sir can u tell me what things i need to study first to learn tensors 🙏🙏🙏pls sir

[@EugeneKhutoryansky]

Chandra, I have a video on tensors at kzbin.info/www/bejne/eZ3MiGqhiN2rjbc

[@CinemaRockPizza]

"Do not worry if you do not understand this"

[@gamelover1079]

Epic😂🤣🤣🤣

[@lil_ToT-XFZ1]

Ez though

[@raphaelfrey9061]

Youll understand it pretty soon if you watch more of eugene khutoryansky

[@yyy76yyvhxxffb32]

I just hate the fact that they make it seem so difficult but in reallity its not

[@EugeneKhutoryansky]

If you like this video, you can help more people find it in their KZbin search engine by clicking the like button, and writing a comment. Thanks.

[@UnforsakenXII]

+Physics Videos by Eugene Khutoryansky Will do!

[@godsadog]

+Physics Videos by Eugene Khutoryansky Excellently explained.

[@markpankiw5430]

I am posting your videos all over face book and to the Chemistry study group !! thanks a million :D

[@EugeneKhutoryansky]

Thanks!!!

[@malikumair5223]

Physics Videos by Eugene Khutoryansky very usefull

[@slipknnnot]

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.

[@vennessalorret5098]

HI..

[@rickandelon9374]

really agreed there must be electronic text books in near future!!

[@Ag89q43G0HyA]

I dont understand 2d draws. I cant imagine the animations.

[@iftakharalam1650]

before anyone watches this video, one should be familiar with the content of quantum physics.

[@ishworshrestha3559]

Ok

[@malikmaricar]

Eugene, you are godlike. If I had seen this before my quantum and classical mechanics classes this semester it would make them way more awesome.

[@ClawsByCaseyYouTube]

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!!

[@cliffordwilliams9597]

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!

[@parjohansson3118]

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:-)

[@rbettsx]

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.

[@vv13346]

Just discovered these excellent visualizations and the first thing I thought of was Susskind's lectures.

[@OmnipotentO]

Whoa I just bought that book

[@LuisCurrupaki]

Awesome way of explaining the quantum realm, another great video Eugene, thank you very much!

[@EugeneKhutoryansky]

+Luís Romano, thanks.

[@dariuszbindacz8022]

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!

[@fizzabatool8803]

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.

[@thanosAIAS]

You sir, are AMAZING!!! Thanks for the awesome videos!!!

[@EugeneKhutoryansky]

+thanosAIAS, thanks for the compliment, and I am glad that you like my videos.

[@iftakharalam1650]

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.....

[@johncamm3853]

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.

[@EugeneKhutoryansky]

Thanks for the compliments about my video.

[@alfakennywon]

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.

[@EugeneKhutoryansky]

+Joe S, thanks for the compliment about my videos.

[@joshlaurienzo6877]

Your videos are always so informative, while remaining intuitive and simple! Thank you for sharing your knowledge and talent!

[@EugeneKhutoryansky]

+Josh Laurienzo, thanks for the compliment. I am glad that you like my videos.

[@malchicken]

Amazing. You are amazing. I have never seen a complicated topic so well explained.

[@tristanjohnson5247]

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

[@EugeneKhutoryansky]

Thanks for the compliment. I make all the animations for my videos myself. I have a friend who does the narration for me.

[@0jaza0]

This is the video I've been looking for since I began to understand wavefunctions. Thank you.

[@EugeneKhutoryansky]

Glad my video was what you were looking for. Thanks.

[@dineshthakare4579]

I'm very happy and thankful to you from my depth of my heart. please upload all the videos regarding quantum mechanics.

[@rahulshaw9051]

This is best video on KZbin for operators,very well explain,keep up the good work.

[@dexterpagnini1145]

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.)

[@EugeneKhutoryansky]

Thanks for the compliment.

[@Daitor3]

Amazing! You succeed in making quantum mechanics very clear, bravo

[@EugeneKhutoryansky]

+Daitor3, thanks.

[@universumpi]

Great video! And your 3D charts are awesome and very helpful.

[@EugeneKhutoryansky]

+universumpi, thanks.

[@thevgancheetah]

This is just SOOO GOOOOD!!!! Couldnt be any better!! Please keep doing whatever you are doing.

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@astralacuity]

It's very nice to have such a clear visualization of the wave function!

[@EugeneKhutoryansky]

+James Hansen, Thanks.

[@Smooth_Manifold]

Perfect explanation!! And Bach's second french suit in the background makes it even better!! BRAVO!

[@EugeneKhutoryansky]

+Dimitris Xatzis, thanks. Glad you liked my explanation.

[@manojnag6984]

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.

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@chintachinakoteswararao2897]

There is always a hidden beauty in these videos.

[@EugeneKhutoryansky]

Thanks.

[@peterazcueattolini481]

What a world class explanation. Gorgeous and elegant. Demystifying.

[@EugeneKhutoryansky]

Thanks for the compliment about my explanation.

[@chuckfaber7521]

Thank you for this video. This helps me understand operators a lot better.

[@rtpcr3969]

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.

[@Klapperklaus84]

could't have said it better!

[@EugeneKhutoryansky]

+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.

[@Klapperklaus84]

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.

[@parjohansson3118]

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!!!

[@EugeneKhutoryansky]

+Pär Johansson, I am glad you liked it. Thanks.

[@vishnusukumaran684]

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

[@EugeneKhutoryansky]

Glad to hear my video was useful.

[@rodrigoappendino]

Your best video. No doubt. I'm very happy to watch this. I never understood very well the concept of operators.

[@ripsirwin1]

Beautiful. These videos continue to impress!

[@EugeneKhutoryansky]

+ripsirwin1, thanks.

[@ambikasaxena1]

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...

[@EugeneKhutoryansky]

Thanks for the compliment about my videos. Advanced topics need fancy graphics too. :)

[@dannycrofts8138]

Thank you... you've really expanded my knowledge of particle physics 😍👍🏽

[@WilliamDye-willdye]

I found this channel because of a comment you left on a Fermilab video. Happy to subscribe!

[@EugeneKhutoryansky]

+William Dye, happy to have you as a subscriber. Thanks.

[@Filopon]

Congratulations, your work is beautiful and easy to understand your explanations. Thanks.

[@EugeneKhutoryansky]

+Juan Filopon, thanks for the compliment.

[@thephysicistcuber175]

I think it's amazing to even try to teach people some basics of the math behind modern physics theories!

[@EugeneKhutoryansky]

+The Physicist Cuber, it is not so bad if it is done with colorful 3D animations. :)

[@thephysicistcuber175]

+Physics Videos by Eugene Khutoryansky ikr

[@derekojeda6861]

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!

[@trolbol1344]

Amazing!! I am a physics student and struggling with quantum mechanics. This and your other videos are tremendously helpful!! thanks!

[@EugeneKhutoryansky]

+Trolbol, thanks. I am glad that my videos have been helpful.

[@darkslayer175]

Outstanding work! Keep up the great effort.

[@EugeneKhutoryansky]

Thanks for the compliment. More videos are on their way.

[@mrx42]

Best video sofar !Great music, great letters used in the title, great animations.

[@ramaswamibalakrishnan1103]

very well described. beautiful pleasing narration.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@StephenGillie]

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.)

[@shehabmahmoud8177]

Finally I am starting to understand what i am taught thanks alot keep it up 😊 best quantum mechanics explanation 😊

[@pekhotinyets]

This guy's videos are beautiful. I haven't seen anything like these anywhere else.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@aSeaofTroubles]

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

[@EugeneKhutoryansky]

+Andy, thanks for the compliment.

[@aSeaofTroubles]

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.

[@anjalikm7166]

Even though I cannot understand the whole concept, it is really good. Keep uploading video. Respecting your effort 😍 😍 😍

[@EugeneKhutoryansky]

Thanks. More videos are on their way.

[@shashankpandey2056]

Thank you so much.These animation are amazing and irreplaceable.

[@EugeneKhutoryansky]

Thanks for the compliments.

[@gerardrbain1972]

Thank you for uploading this video.

[@EugeneKhutoryansky]

+gerard bain, thanks.

[@1971jwing]

Wow something just popped in my brain while observing this. Hope it wss me getting better intuition lol. Amazing and thank you.

[@cameronspalding9792]

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

[@OmegaPsiPhi0]

I love Eugene she always so elegantly explains the math xxx

[@EugeneKhutoryansky]

Thanks.

[@antoniocampos9721]

This is sublime, your voice is perfect.

[@EugeneKhutoryansky]

Thanks. The narration is done by my friend, Kira Vincent.

[@hakkbak]

what a coincidence I was just revising quantum mechanics and you made this video. very impressive and insightful video as always

[@EugeneKhutoryansky]

+hakkihan tunbak, thanks.

[@ricardocesargomes7274]

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!

[@EugeneKhutoryansky]

You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link: kzbin.info_video?ref=share&v=LZie2QC5Jbc You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately. Details about adding translations is available at support.google.com/youtube/answer/6054623?hl=en Thanks.

[@abubakramin6710]

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

[@adriancoronel5119]

Quantum Operators,magnifica explicación,excelente presentación,brillante la calidad de este video,the music is beautiful,thanks very much,greetings from México.

[@EugeneKhutoryansky]

Thanks.

[@quinnsq]

If you're looking for an idea, a video on ladder operators would be splendid.

[@MissionTrueLove]

Thank you for this beautiful and easy explanation

[@EugeneKhutoryansky]

Thanks. I am glad you liked my explanation.

[@jaimelima2420]

This is really useful to understand Digital Signal Processing (DSP) concepts more deeply.

[@user-pk7ih2ej9s]

Your videos are awesome!!! I've learned so much~

[@EugeneKhutoryansky]

+梁育誌, thanks. I am glad to be able to help.

[@mahendrasinghadhikari5771]

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.

[@RomaEsperanto]

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!

[@EugeneKhutoryansky]

+RomaEsperanto, thanks for the compliment. I am glad you liked my video, and I am glad to have you as a subscriber.

[@JiYesYouTube]

Great graphical illustration of Quantum Operators on Wave Functions. All complexities associated with Quantum Mechanics and Complex Quantum Operators simplified through animations.

[@EugeneKhutoryansky]

Thanks for the compliment.

[@maarsalah3952]

Amazing video,I hope that you focus more on the fondamentale Côté of Avery equations of quantum physics,merci pour les efforts

[@canys24bb78]

This chanel is amazing. I love all your explanations on quantum mechanic. You're helping me a lot. Tnx so much 😘😘😘

[@EugeneKhutoryansky]

Thanks.

[@diptendumandal8354]

This is quite helpful.... atleast helps us visualise the mathematics associated. Waiting for more videos! Amazing!

[@EugeneKhutoryansky]

Glad my videos are helpful. More are always on the way. Thanks.

[@zhengqunkoo]

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.

[@jaimelima2420]

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….

[@abubakramin6710]

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

[@EugeneKhutoryansky]

Glad my video was helpful. Thanks.

[@abubakramin6710]

@@EugeneKhutoryansky good luck maam

[@60pluscrazy]

Amazing visual explanation 👌

[@EugeneKhutoryansky]

Thanks for the compliment.

[@physicsenthusiast9233]

This video is cool, its very important and beneficial for students like us. Thank you for such great video.:)

[@EugeneKhutoryansky]

+Sangeet Chand, you are welcome and thanks.

[@clieding]

Great video; very informative- thank you!

[@the0dued]

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.

[@EugeneKhutoryansky]

+jamie .willis, glad my video was helpful. Thanks.

[@shivamsinghaswal4995]

Beautiful work. Please keep it up!

[@EugeneKhutoryansky]

Thanks for the compliment.

[@StoicFlame]

your videos are cool, you explain things easily and slowly

[@EugeneKhutoryansky]

+The whisperer, thanks.

[@realcygnus]

superb quality content ! as always

[@EugeneKhutoryansky]

+realcygnus, thanks. Glad you liked it.

[@tj8870]

+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.

[@rodolfocarvalho880]

very very good. Thank you very much, Rodolfo (Brazil)

[@TheNoBSZone]

These are so beautiful... Thank you

[@EugeneKhutoryansky]

+TheNoBSZone, thanks for the compliment.

[@venceslas2681]

ich weine, ich bin bin so glücklich dieses video gesehen zu haben. Thank you very much thank you thank you thank you and thank you

[@joeandcoffee]

Thank you so much for the video,Eugene. I really wish our quantum mechanic book is as clear and detailed (with an image) as this video.

[@EugeneKhutoryansky]

Thanks. Glad you liked my video.

[@abubakramin6710]

Nice videos great explanations

[@musicoscope]

Thank you! Wonderful videos!

[@EugeneKhutoryansky]

Thanks. I am glad you like my videos.

[@firegeek22]

Thank you for the fantastic videos!

[@EugeneKhutoryansky]

+Eddy O'Reilly, I am glad that you like them. Thanks.

[@kat_064]

Thanks for such an amazing vedio.....please keep doing what you have started

[@EugeneKhutoryansky]

Thanks. More videos are on their way.

[@DEEPAK619wwe]

I AM FAN FOR YOUR THINKING FOR PRESENTING

[@faisalkabir7363]

great effort to help us visualize quantum mechanics.

[@EugeneKhutoryansky]

Thanks.

[@Russocass]

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.

[@EugeneKhutoryansky]

+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.

[@shilpamishra3817]

I agree with JRusso.

[@shilpamishra3817]

I would want him speak also. I want to hear how he sounds. Eugene has some profound videos up there and I guess he sounds full of depth too!

[@tixe87544]

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)...

[@SchoolTV92]

great video explaing concept of wave function. good work

[@EugeneKhutoryansky]

Thanks for the compliment.

[@derciferreira7211]

watching this video I took a step furtyher! thank you!

[@noelwalterso2]

Love your choice of music.

[@EugeneKhutoryansky]

Thanks.