Uploads from Dr. Jorge S. Diaz

Currently Playing: Action-angle variables: the three-body problem and Quantum theory

Buy me a coffee and support the channel: https://ko-fi.com/jkzero [Members only] Supplementary Notes with all the equations and extra content https://ko-fi.com/jkzero/shop Become a member and get access to the Supplementary Notes with all the equations and extra content https://ko-fi.com/jkzero/tiers Action-angle variables are a special type of canonical transformation ideal for the study of periodic systems. In this video, we explore its origins in Lunar perturbation theory (Delaunay), its further development by Poincaré, and its final formalization in classical mechanics by Schwarzschild. Schwarzschild's theory included a direct adaptation to the use of this method in quantum theory, leading to the fundamental Bohr-Sommerfeld quantization of the atom and the rule that allowed Heisenberg the creation of modern quantum mechanics. [Related videos] ∘ Canonical Transformations: The bridge to quantum mechanics https://youtu.be/wVqqj6N_7RA ∘ Poisson bracket: a step before Quantum Mechanics https://youtu.be/Be3vSBTPTTI ∘ Phase Space: the geometry of Hamiltonian mechanics https://youtu.be/IVQRfHAgLxk ∘ Atomic fine structure: the true story https://youtu.be/H4ZnVpiQTDw ∘ The virtual orchestra of quantum mechanics https://youtu.be/UbFrVCYDANg ∘ This is how Heisenberg created quantum mechanics https://youtu.be/oVzzIkkYGY8 ∘ The birth of Quantum Mechanics https://youtu.be/XQAAU11DbDI [References] ∘ M. Delaunay, "Théorie du Mouvement de la Lune," Paris (1860) https://books.google.de/books?id=kS8pcnlVN9wC ∘ M. Delaunay, "Théorie du Mouvement de la Lune," MNRAS 21, 80 (1861) https://doi.org/10.1093/mnras/21.3.80a ∘ H. Poincaré, "Sur le problème des trois corps et les équations de la dynamique," Acta Math. 13, 1–270 (1890) https://www.mittag-leffler.se/about-us/history/prize-competition/ ∘ M. Planck, "Über das Gesetz der Energieverteilung im Normalspectrum," Verh. Dtsch. Phys. Ges. 2, 237–245 (1900) ∘ M. Planck, "The genesis and present state of development of the quantum theory," 1918 Nobel Prize Lecture (1920) https://www.nobelprize.org/prizes/physics/1918/planck/lecture/ ∘ K. Schwarzschild, "Zur Bahnbestimmung nach drei Beobachtungen" Astron. Nachr. 124, pp. 211–216 (1890) ∘ K. Schwarzschild, "Methode zur Bahnbestimmung der Doppelsterne" Astron. Nachr. 124, pp. 215–218 (1890) ∘ M. Planck, "Loi du Rayonnement Noir," Proceedings of the First Solvay Conference in Physics, p.93 (1912) ∘ A. Sommerfeld, "Die Bedeutung des Wirkungsquantums fur unperiodische Molekularprozesse in der Physik," Proceedings of the First Solvay Conference in Physics, p.313 (1912) ∘ J. L. Sanders and J. Binney, "Actions, angles and frequencies for numerically integrated orbits," MNRAS 441, 3284 (2014) https://doi.org/10.1093/mnras/stu796 ∘ K. Schwarzschild, "Zur Quantenhypothese," Sitzungsberichte der Preußischen Akademie der Wissenschaften in Berlin, pp. 548-568 (1916) ∘ C. Foster et al. "Kinematics and simulations of the stellar stream in the halo of the Umbrella Galaxy," MNRAS 442, 3544 (2014) https://doi.org/10.1093/mnras/stu1074 ∘ A. Sommerfeld, "Zur Theorie der Balmerschen Serie," Klasse der K.B. Akademie der Wissenschaften zu München, 425 (1915) ∘ P.S. Epstein "Zur Theorie des Starkeffekts," Phys. Z. 17,148 (1916) ∘ W. Heisenberg, "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen," Z. Phys. 33, 879 (1925) ∘ M. Born and P. Jordan, "Zur Quantenmechanik,” Z. Phys. 34, 858 (1925) ∘ P.A.M. Dirac, "The fundamental equations of quantum mechanics," Proc. R. Soc. Lond. A109, 642 (1925) https://doi.org/10.1098/rspa.1925.0150 [Credits] Solutions to the three-body problem by Perosello under CC BY-SA 4.0 Charles Eugene Delaunay, public domain Eiffel tower by B.L. Song, public domain Names on southeast side of the Eiffel Tower by Juanedc under CC BY 2.0 Earth, Moon, and Sun by A. L. Blue, free use via Vecteezy https://www.vecteezy.com/video/11038661-the-earth-moon-and-sun-in-starry-space Vector model of orbital angular momentum by Maschen, public domain Frankfurt Senckenbergianum, public domain Paul Epstein, public domain Strasbourg University, public domain Giant red spot by A. Mimi, free use via Vecteezy https://www.vecteezy.com/video/51270680-a-breathtaking-view-of-the-gas-giant-and-its-celestial-companions-its-swirling-storms-and-iconic-red-spot Karl Schwarzschild in his working place, public domain Animation of 4179 Toutatis's orbit by Phoenix7777 under CC BY-SA 4.0video/51078673-an-abstract-loop-animation-with-fractal-pattern-movements Neptune Moon Dance by NASA/JPL Orbital eccentricity by Phoenix7777 under CC BY-SA 4.0 Black hole visualization, by NASA/J.Schnittman, public domain Rutherford atom animation, by G. Creador under CC BY 3.0 Grave of Karl Schwarzschild by Julian Herzog under CC BY 4.0 AIP: American Institute of Physics, Emilio Segrè Visual Archives CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/deed.en CC BY 4.0: https://creativecommons.org/licenses/by/4.0/deed.en