21. Addition of Angular Momenta - the Clebsch-Gordan Coefficients | Weinberg’s Lectures on QM скачать в хорошем качестве

21. Addition of Angular Momenta - the Clebsch-Gordan Coefficients | Weinberg’s Lectures on QM

#QuantumMechanics #StevenWeinberg #AngularMomentum 0:00 - Introduction 2:54 - Expressing Total Angular Momentum States in terms of Constituent States 5:36 - Definition of Clebsch-Gordan Coefficients 6:45 - Why Do We Study Total Angular Momentum States? 9:19 - Calculating Clebsch-Gordan : The Highest Weight State 11:47 - Weinberg’s Convention for Clebsch-Gordan Coefficients 12:55 - Adding 2 Angular Momenta can result in more than 1 multiplet 14:22 - Generate a Total Angular Momentum Multiplet with Lowering Operator 17:48 - Graphical Rep. of Total Angular Momentum states : Beginning of a new Multiplet 19:25 - Verifying the new Highest Weight State 22:00 - Finding all multiplets from the composition of 2 23:56 - Finding the minimum value of j 24:51 - Multiplicity of m increases by 1 with each step of lowering : Proof 28:03 - Complete Algorithm for finding all Multiplets 31:19 - Useful matrix properties of Clebsch-Gordan Coefficients 35:19 - One more non-trivial example of Clebsch-Gordan Coefficients 38:15 - Applications to Atomic Spectral 41:52 - Fine Structure : Spin-Orbital Coupling 46:32 - The Lamb Shift 49:18 - Hyperfine Structure : Spin-Spin Coupling 50:28 - Relation between Spin and Magnetic Moment 55:01 - 21 cm Hydrogen Line 56:48 - Ending This is lecture 21 of the series (part 3 of Chapter 4), where we discuss and explain the book, “Weinberg’s Lectures on Quantum Mechanics”. Last time, we discuss a general method to construct a single angular momentum multiplet, just from rotation algebra. In this video, we shall show how to combine 2 angular momenta multiplets, to form new total angular momentum multiplets. As we shall see, more than 1 multiplet, each with different values of the quantum number “j”, will result from such a combination. This is what we meant by addition of angular momenta. The key problem is to solve for the total angular momentum states, which are expressed in linear combinations of the product of its constituent multiplets. The coefficients in such expansions, are known as the Clebsch-Gordan coefficients; and we shall spent much of this lecture solving them. A general algorithm will be introduced, that will allow us to derive all the multiplets that can result from the combination of 2 angular momentum multiplets. Finally, we will go through some applications of the angular momentum states to the atomic spectral; and talk about important topics such as : the fine structure, hyperfine structure and the Lamb shift… ► Weinberg’s book on Quantum Mechanics https://amzn.to/46msMA9 (This my affiliate link. As an Amazon Associate I earn from qualifying purchases.) ►Generating a single angular momentum multiplet(Lecture 20):    • 20. Angular Momentum States/Values From Co...   ►Next(Lecture 22)    • 22. Spin and the Stern-Gerlach Experiment ...   ►Full Quantum Mechanics playlist:    • Weinberg's Lectures on Quantum Mechanics   Some more good books for your physics reading list : Here are my affiliated links(As an Amazon Associate I earn from qualifying purchases.) ►Susskind’s Theoretical Minimum series : 1.) Classical Mechanics : https://amzn.to/47HPpiV 2.) Quantum Mechanics : https://amzn.to/48qO6ph 3.) Special Relativity and Classical Field Theory : https://amzn.to/3I5tvvO 4.) General relativity : https://amzn.to/48rNcZv ►Landau & Lifshitz series : 1.) Mechanics : https://amzn.to/48BSMtk 2.) The Classical Theory of Fields : https://amzn.to/48uOYc9 3.) Quantum Mechanics: Non-Relativistic Theory : https://amzn.to/3uJkw0j 4.) Quantum Electrodynamics : https://amzn.to/3T4XGtf 5.) Statistical Physics, Part1 : https://amzn.to/49nTfiT 6.) Fluid Mechanics : https://amzn.to/49mAPPI 7.) Theory of Elasticity : https://amzn.to/42M65oF 8.) Electrodynamics of Continuous Media : https://amzn.to/42Jve3v 9.) Statistical Physics, Part2: Theory of the Condensed State : https://amzn.to/3SKU6TJ 10.) Physical Kinetics : https://amzn.to/3OQ7c0Q ►Greiner series : -Classical Theoretical Physics : Classical Mechanics: Point Particles and Relativity : https://amzn.to/48uPqqR Classical Mechanics: Systems of Particles and Hamiltonian Dynamics : https://amzn.to/48iLREm Classical Electrodynamics : https://amzn.to/3uyhGeC Thermodynamics and Statistical Mechanics : https://amzn.to/3I95ELU -Theoretical Physics : Quantum Mechanics: An Introduction : https://amzn.to/42R0Sfl Quantum Mechanics: Special Chapters : https://amzn.to/48m7C65 Quantum Mechanics: Symmetries : https://amzn.to/3SEx4Og Relativistic Quantum Mechanics : https://amzn.to/3I7LgdS Field Quantization : https://amzn.to/3I5bVIr Quantum Electrodynamics : https://amzn.to/3wgGqbx Quantum Chromodynamics : https://amzn.to/49JuxJU Gauge Theory of Weak Interactions : https://amzn.to/49IBIlc Nuclear Models : https://amzn.to/3I3rWP4