Clebsch–Gordan Coefficients Explained

In this video, we will talk about Clebsch-Gordan coefficients. We'll discuss their definition, and explain how to use them.

Clebsch-Gordan coefficients are named after the German mathematicians Alfred Clebsch and Paul Gordan. The coefficients are defined like this: Clebsch-Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis.

00:00 Introduction
00:14 Definition
00:29 Coupling Angular Momenta
01:11 Product Basis
01:33 Coupled Basis
02:26 Mathematical Background
03:05 How to Use Them?
04:01 4 Steps to CG Coefficients
04:38 Example 1
05:06 Example 2
05:30 Example 3
05:49 Hidden Zeroes
06:21 Going Both Ways

References:
[1] Sakurai, "Modern Quantum Mechanics"

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[j.abrahamhernandez]

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

[yummy-mochi]

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

[alexxthalio]

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.

[KamranKhan-oult]

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.

[bornajukic]

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

[bhupendrasharma]

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

[sanjuktapaul]

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

[hiZarki]

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

[tasnimulsarwar]

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.
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[armandoski-g]

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

[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.

[thjabi]

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

[adreesu]

You have simply nailed it man. Thumbs up.

[saharbehroozinia]

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

[rafabenavent]

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

[eliyahomar]

Thank you so much, cannot expect better explanation than this

[Zxv]

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

[polvega]

This video is an utterly godlike explanation, thank you.

[alexd]

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