11. Spherical Harmonics - Eigenfunctions of Angular Momentum | Weinberg’s Lectures on QM скачать в хорошем качестве

11. Spherical Harmonics - Eigenfunctions of Angular Momentum | Weinberg’s Lectures on QM

#quantummechanics #StevenWeinberg #sphericalharmonics 0:00 - Introduction 0:58 - Eigenfunctions & eigenvalues of L_3 4:24 - Spherical Harmonics are Homogeneous Polynomials : Proof 6:16 - Relation between the quantum numbers “m” & “l” 9:52 - Deriving the Laplace equation for Spherical Harmonics 12:43 - Counting number of degrees of freedom in Spherical Harmonics 18:07 - Examples : Solving for Spherical Harmonics(l = 0) 18:39 - Examples : Solving for Spherical Harmonics(l = 1) 20:32 - Examples : Solving for Spherical Harmonics(l = 2) 25:55 - Ending This is lecture 11 of the series (part 5 of Chapter 2), where we discuss and explain the book, “Weinberg’s Lectures on Quantum Mechanics”. In this lecture, we continue our discussion of the states of a particle in a central potential. In the last lecture the eigenvalues of L^2 are found, now we shall solve for its eigenfunctions; the spherical harmonics. These functions are shown to be homogeneous polynomials in cartesian coordinates; using the alternate form of L^2, found in lecture 10. A Laplace equation for spherical harmonics is derived. This is an equation equivalent to the eigenfunction equation of L^2, but is easier to work with. Using this equation, we shall solve for a few examples of the spherical harmonics. By the end of this lecture, the eigenfunction problem of angular momentum, will be completely solved… ► Weinberg’s book on Quantum Mechanics https://amzn.to/46msMA9 (This my affiliate link. As an Amazon Associate I earn from qualifying purchases.) ► Alternate form of L^2 (lecture 10) :    • 10. Finding the Eigenvalues of Angular Mom...   ► Lecture 12 :    • 12. Orthonormality Relations of Spherical ...   ► Lecture 10 :    • 10. Finding the Eigenvalues of Angular Mom...   ► Full 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