20. Angular Momentum States/Values From Commutators | Weinberg’s Lectures on Quantum Mechanics скачать в хорошем качестве

20. Angular Momentum States/Values From Commutators | Weinberg’s Lectures on Quantum Mechanics

#QuantumMechanics #StevenWeinberg #AngularMomentum 0:00 - Introduction 3:27 - Ladder Operators : A Reminder 5:57 - Angular Momentum Ladder Operators 8:56 - Some Commutators of Angular Momentum 11:00 - Eigenvalues of J^2 are positive 12:32 - Eigenvalue of J^2 ≥ (J_3)^2 13:15 - Solving f^2 in terms of j 17:29 - Showing that the Highest Weight State is unique 19:24 - Proving j’ = -j (j’ is min. m) 22:21 - Counting states in j-multiplet/the allowable values of “j” 24:38 - Normalisation of jm-states : phase convention 30:52 - Solving the matrix elements of J / Eg. Pauli matrices 36:03 - An Important Theorem on Inner Products in j-Multiplet 39:01 - Ending This is lecture 20 of the series (part 2 of Chapter 4), where we discuss and explain the book, “Weinberg’s Lectures on Quantum Mechanics”. In this video we shall give a derivation of all the eigenstates and eigenvalues of angular momentum; using just the algebra of rotations. The results are general and apply to all representations of rotation. It is shown that the angular momentum quantum number, j, can either be integer or half-integer values. This is a well-known and important result in quantum mechanics. All these are accomplished, by using the angular momentum analog of the ladder operators, introduced in lecture 17 for the harmonic oscillator… ► Weinberg’s book on Quantum Mechanics https://amzn.to/46msMA9 (This my affiliate link. As an Amazon Associate I earn from qualifying purchases.) ►Ladder Operators For Harmonic Oscillator(Lecture 17)    • 17. Quantum Harmonic Oscillator | Weinberg...   ►Next (Lecture 21)    • 21. Addition of Angular Momenta - the Cleb...   ►Previous (Lecture 19)    • 19. Introducing Spin, Rotations and Group ...   ► Full Quantum Mechanics course :    • 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