Clebsch–Gordan Coefficients Explained

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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 • [2] http://pdg.lbl.gov/2019/reviews/rpp20... • [3] https://en.wikipedia.org/wiki/Clebsch... • Follow us on Instagram: / prettymuchvideo • If you want to help us get rid of ads on YouTube, you can support us on Patreon! • / prettymuchphysics

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