Clebsch-Gordan Coefficients Explained

[@j.abrahamhernandez3629]

what most lecturers fail to accomplish in hours of lecture you did so in less than 7 minutes - respect!

[@PrettyMuchPhysics]

Thank you very much! That‘s exactly what we want to achieve with our videos!

[@yummy-mochi420]

Quite possibly the most powerful, efficiently succinct piece of media I've ever come across. Just, wow. Actually speechless. So much respect.

[@PrettyMuchPhysics]

Thank you very much for such a high praise! We're glad you liked it! :)

[@alexxthalio7054]

my dude it's almost gross how much better your video explains this then a lecture. 10/10 great job

[@Tomtomtomahawk]

Massive thanks, recommended your very well made video to all my classmates. I went from no idea of how to use Clebsch-Gordan coefficients to solving the question of my homework watching your video.

[@PrettyMuchPhysics]

That‘s great, that‘s exactly what we want to achieve with our videos!! :D And thanks for recommending our videos, this helps a lot!

[@KamranKhan-ou2lt]

A very simple explanation of how to find the CG coefficients. It is always a headache topic for me. Thanks to your video, it makes my day.

[@PrettyMuchPhysics]

Thank you very much! :)

[@bornajukic7712]

I just want say "thank you" for this beautiful video. Student of physics from Croatia

[@PrettyMuchPhysics]

Thank you very much! Comments like yours mean a lot to us!

[@hiZarki]

saving this vid for whenever I have doubts. great, clear explanation.

[@PrettyMuchPhysics]

Thank you 😊

[@bhupendrasharma2705]

Such a heroic task you have accomplished in approximately 7 minutes! God bless you! #Physics_Student_From_Nepal

[@PrettyMuchPhysics]

Thank you very much! :)

[@armandoski-g]

Best video on CG. Fast and simple explanation, thanks for your effort!

[@sanjuktapaul9841]

Thank you so much! You could cure my phobia for CG coefficients from my Masters days. Subscribed and wishes from India.

[@PrettyMuchPhysics]

Thank you for your nice comment! :)

[@rafabenavent927]

Esto es magnífico!! Gracias! Student of physics from Spain

[@PrettyMuchPhysics]

Thank you very much! We‘re glad you liked it!

[@tasnimulsarwar9189]

Absolutely marvelous. It felt like I was listening to a piece of work by Mozart himself. The seemless way you explain things and the lucid path you take is like blending of all the instruments in a music ensemble. Loved this so so much. Thank you so much for this. Just subscribed. Hoping for more such videos.

[@PrettyMuchPhysics]

I think that‘s one of the nicest comments we’ve ever gotten, thank you :) we have a huge list of video ideas that we want to cover, so stay tuned! :D

[@th3jabi]

tysm brother that table was driving me crazy until I found your video 🛐🛐🛐

[@zapphysics]

Just finishing up an SU(2)-heavy project for research and this video had me in a cold sweat lol. Nice video, good explanation, and gotta love the PDG.

[@tanchienhao]

Your project sounds cool! Could you briefly summarise what it was about? :)

[@PrettyMuchPhysics]

Thanks for the kind words Zap :)

[@adrees4u]

You have simply nailed it man. Thumbs up.

[@polvega1236]

This video is an utterly godlike explanation, thank you.

[@eliyahomar]

Thank you so much , cannot expect better explanation than this

[@PrettyMuchPhysics]

Wow, thank you very much! Glad you liked it!

[@saharbehroozinia9700]

How perfect you are and how lucky I am that I found this video before my exam :)

[@PrettyMuchPhysics]

Thank you! :D Good luck with your exam! 👍

[@paugarciagulisano7967]

Less than 7 minutes were enough to explain one of the hardest topics of QM. Thank you so much!

[@armalify]

Great. Keep it all simple, clear, and connected, then you will get a beautiful video like this...

[@PrettyMuchPhysics]

Thank you very much! :)

[@boulderink]

Thanks for the excellent and concise demonstration

[@PrettyMuchPhysics]

:)

[@442277100]

BRO U SAVED MY LIFE 😱 THANK YOU PHYSICS MAN

[@husseinghanim4517]

No words enough to thank you these really excellent work it gives sense for every thing

[@PrettyMuchPhysics]

We are really glad to hear that! Thanks for watching! :)

[@fbstore9972]

Great sir! Well explained in just 7 minutes! Greetings from India ❤

[@PrettyMuchPhysics]

Thanks! :D

[@Zxv975]

God I wish this video was out when I was doing my masters course on this topic. Amazingly clear video as always and thanks for that cool reference. Looking forward to the derivation video! The whole SU(2) spin theory is something I just never completely wrapped my head around, and I've been meaning to derive from "first principles" for awhile now. This video series will save me the trouble of trawling through a textbook on my own :p

[@PrettyMuchPhysics]

I hope our videos can fulfil your expectations, we'll give our best!

[@Mystixor]

Thanks for explaining what our profs wouldn't!

[@PrettyMuchPhysics]

:)

[@alexd3271]

Thank you! Best explanation ever on CG coefficients table. I guess lecturers don't want you to understand it so that you can suffer in silence deriving them lol

[@PrettyMuchPhysics]

Haha maybe, who knows! But anyway, thanks for the nice feedback!

[@alexd3271]

@@PrettyMuchPhysics You're welcome! I just checked your channel: straight-to-the-point and simple explanations. I am looking forward to support you and share with my friends. Keep it going ;) Physics student from UK. P.S.: I'd suggest to hire an Instagram marketing service (like on fiverr etc.) or learn about branding, paid-campaigns and that sort of stuff. If well done it works magic.

[@PrettyMuchPhysics]

Thanks for the kind words, that means a lot! We‘ll look into it!

[@pedromadrid6234]

Great video! Clear as water! You explain very well! Thanks!

[@PrettyMuchPhysics]

Thank you very much for your nice comment! :)

[@abhijith.science1677]

Dude, that's an amazing explanation

[@PrettyMuchPhysics]

Thank you very much! :)

[@antoniocotarodriguez5732]

Thanks! in only seven minutes that's amazing

[@PrettyMuchPhysics]

Thank you! That‘s what our channel is all about! 🥳

[@lowroar5127]

These videos are great. Thanks a lot and keep them coming!

[@PrettyMuchPhysics]

Glad you like them! We will definitely make a lot more! :D

[@milicitrus]

Amazing video, cheers from Mexico

[@PrettyMuchPhysics]

Thank you very much!

[@ankitagarg6432]

You saved my life sir🙏thank you so much

[@ankitagarg6432]

Love from india

[@PrettyMuchPhysics]

That‘s great to hear, we‘re glad that our video was useful to you! :)

[@erikasgrim2871]

Amazing video. Thank you very much.

[@PrettyMuchPhysics]

Thanks!! 🙂

[@vairoalexnder]

first, thanks for this amazing video, second i want to ask have you made the different videos where you derive clebesh Gordon coefficients , and if yes what is link and thanks

[@PrettyMuchPhysics]

Thank you very much! We derived the CG coefficients for the simplest case (coupling 1/2 with 1/2) here: kzbin.info/www/bejne/l2fTkGuAZraHrdk Note that this is just for educational purposes, for "real world" calculations, you should refer to a table like the one by the particle data group!

[@vairoalexnder]

@@PrettyMuchPhysics thanks so much, I really appreciate your reply, but I wonder do you have any video that explains quantum angular momentum L and m ??

[@sarahjoyce9159]

great explanation!! thank you so much:)

[@PrettyMuchPhysics]

Thank you!

[@ReyJuanOrtiz]

¡Excelente vídeo! ¡saludos desde México!

[@PrettyMuchPhysics]

Thank you very much! :D

[@adriataveira]

this helped soo much! thank you ❤️

[@PrettyMuchPhysics]

Great! :D Thanks for your nice comment!

[@dartz2234]

Man that was very very helpful, thanks alot 💓💓💓💓

[@PrettyMuchPhysics]

Glad you liked it, thanks for watching!! :)

[@pia31415]

Good video. It helped me read the information off the table. I don't get why the individual sections of the table are organized in that way though? Couldn't they be separate little tables rather than touching each other? (Take the 1x1 table for example)

[@PrettyMuchPhysics]

In case of the 1x1 table, those nine states on the left constitute one complete basis system of the product basis, similarly, the nine states on top together are the complete coupled basis. Therefore, they belong together. As we mentioned in the video, this should actually be a square 9x9 matrix, but since most of the entries are zero, they are usually left out.

[@pia31415]

@@PrettyMuchPhysics thanks so much! That sorts it out.

[@lemonbigs6087]

Great video!

[@PrettyMuchPhysics]

Thank you very much!

[@ww.ww.u]

very good video!

[@lamaabdullah1666]

Thank you so much 😭😭😭😭

[@PrettyMuchPhysics]

Glad you liked it :)

[@238mob8]

Great video

[@Dimwol333]

How would you find the Clebsch-GORDON coefficient for which the total spin is 1/2 and the z-component of the spin is 1? I couldn't locate that on the table?

[@Dimwol333]

Also, the spin of particle 1 is 1 and spin of particle 2 is 1/2.

[@PrettyMuchPhysics]

The magnetic quantum number (m) cannot be larger than the orbital quantum number (l), that's why there is no L=1/2, M=1 column. In other words, if it's not in the table, it's zero!

[@luisenriquequisperojas9361]

I really love you man, you made my day. Now I can stop crying hahaha

[@PrettyMuchPhysics]

That's the effect we're hoping for with our videos ;D Thanks for the nice words!

[@jerrynews5803]

Excellent !

[@Write_with_me_gknotes]

Thank you so much sir

[@PrettyMuchPhysics]

:D

[@TimschneiderSchneider]

I don't understand why the coupled basis looks the way it does? In my mind it should be |00> |0-1> |01> |10> ....

[@kathystein411]

Makes sense now thx

[@PrettyMuchPhysics]

That‘s great, thanks for watching! :)

[@Nysnassian]

And if you have to calculate them by hand?

[@Uyhn26]

Thank you!

[@PrettyMuchPhysics]

😁

[@peterpan0201]

Thanks!

[@PrettyMuchPhysics]

Wow, thanks for your donation! :O We're glad you liked the video :)

[@saiouln.8060]

Super !!

[@PrettyMuchPhysics]

Thank you! :D

[@ujjwalyadav8780]

In first example j1=3/2 j2=1/2 j is btw |j1-j2| and j1+j2 u took j = 5/2 how is possible??

[@zaharazettira3214]

thankyou sir

[@theorama229]

Hey, there! We've been watching your videos for a while now and would love to discuss an idea with you. Where should we contact you? Best, Adam

[@PrettyMuchPhysics]

You can find our email/Twitter/Instagram info on our channel page!

[@Andrea-kx3zd]

If I have 0×1/2 ?? I don't have to use the table, but I don't know how it works 😅

[@Andrea-kx3zd]

J1×J2 = 0x1/2

[@PrettyMuchPhysics]

@@Andrea-kx3zd If L=0, then the resulting multiplet will be the same as the 1/2 multiplet (since you actually only have one angular momentum, you can't couple anything).

[@Andrea-kx3zd]

@@PrettyMuchPhysics Thank you 😁

[@anthbenit2576]

Is a tensor product same as outer-product ?

[@wondertang1298]

Nope. There's a simple difference. The consequence of tensor product will have a multipled dimension dim=dim1*dim2, but the outer-product is calculated by a determinant and will keep the dimension.

[@hungnguyen-tn5mx]

how did you do it can you share with me , thank you

[@PrettyMuchPhysics]

What do you mean?

[@piyushm2340]

Thanks thanks thanks

[@PrettyMuchPhysics]

You're welcome! :D We're glad you liked it!

[@magalhaes753951]

Don't derive them? Can you tell that to my professor? So much time wasted on exam doing this

[@PrettyMuchPhysics]

🙈

[@pendalink]

I love you

[@Nightfold]

While I think this video is good at what it does, I cannot help but feel frustrated that even after reading the chapter on this on a Quantum Physics book, reading my professor's notes and watching this video, I still don't understand a thing.

[@PrettyMuchPhysics]

Any particular questions? Maybe we can answer them here or in a future video?

[@EverythingScience]

Anyone ever notice how physics people always seem to have wild names? Maybe I'm just an ignorant American and Clebsch isn't wild o.o

[@PrettyMuchPhysics]

I think Clebsch sounds funny in any language :D

[@Lukexxxxxx]

Maybe it helps you that Clebsch and Gordan are not common last names in Germany. I haven't seen these last names a single other time. But then Schrödinger (actually Austrian) and Heisenberg aren't either. Pauli, Born, Stern, Gerlach, Stark are common names.

[@arielkibbey443]

くさんありますありがとうございます」、

[@PrettyMuchPhysics]

😀

[@Lukexxxxxx]

This is a useful video and something that isn't already out there a million times (as most topics of physics related channels are), like your other videos, but I think you are being too sloppy in the notation. You are using a lot of what I call pseudo-math notation. I.e. what you are writing isn't accurate in math terms. You're using = symbols where you should use set notation and "element of". You're just writing a tensor product symbol between (j1,m1) and (j2,m2) at the beginning then an arrow -> that doesn't actually mean anything, you call the tensor symbols "couples to". |J,M> should EQUAL some linear combination of (j1,m1) o (j2,m2). why not write it accurately like this? what's the harm? What you write instead "looks" mathy but isn't accurate. There actually are physicists that do care for having the math straight and who don't like this sloppy way of writing (and it confuses them, because they are trying to make sense of something mathematically and they can't because someone just wrote random symbols). that is really prevalent in physics because a lot of people don't have rigorous math backgrounds and just don't know better, so they use symbols like =>, = etc seemingly randomly and from gut feeling, not according to what they mean.

[@PrettyMuchPhysics]

Good thing this is a physics channel and not a pure math one. What we want to convey is a feeling for what happens physically, the math is just one helpful tool to achieve this goal, next to graphs and diagrams. Our approach is to first understand the underlying physics, and then dabble in the rigorous mathematics. Physics can be performed in several levels of rigor. The more you get to know a topic, the more you can dive into the mathematics, which is something we not only do ourselves, but also definitely endorse. Take quantum mechanics for example. You might agree that it‘s more useful for a physicist to understand the relation between a wave function, the probability density and observables, than it is to first rigorously define the Hilbert space. Rest assured that we do know how tensor products work, or when to use set notation. However, this is a KZbin video, meant to be a smooth introduction to a topic-and not a PhD thesis.

[@Lukexxxxxx]

@@PrettyMuchPhysics I don't understand what the issue is of not writing nonsensical math then (as you did in several places). You should have just written words or drawn a picture rather than use bogus notation that misleads people reading the stuff you've written down. It just sounds like an excuse and a rather thin-skinned reaction to constructive criticism that is obvious and beginner level (not PhD). Most of what you said is beside the point I made. This isn't an argument of making things pedantically mathematical and forgetting the physical meaning behind it.

[@PrettyMuchPhysics]

Don’t get me wrong, we‘re thankful for your criticism! And to summarize: when precise math notation is necessary, we won’t shy away from it (e.g. on our group theory video). But apart from that, we stick to the physicist‘s methods, like treating a derivative as a fraction ;)

[@jrashad]

nerd

[@billydagenham]

sloppy notation has gotten me all the way to a PhD haha

[@manofculture432]

Dislike for the unfortunate "don't derive, refer to table!".

[@PrettyMuchPhysics]

That's just how you should use Clebsch-Gordan coefficients when doing calculations (which this video is about). We might do another video on how to derive them, but it's not very practical to derive them from zero every time.

[@Dimwol333]

THANKS A LOT!!