Uploads from Dr. Jorge S. Diaz

Currently Playing: The bridge to quantum mechanics

Buy me a coffee and support the channel: https://ko-fi.com/jkzero [Free Notes] Get the free notes with all the equations here: https://ko-fi.com/jkzero/shop Canonical transformations are the special changes of phase-space variables that preserve Hamilton’s equations and the structure of classical mechanics. In this video, I present their full theory, beginning with familiar examples like the Kepler problem and the simple harmonic oscillator, describing the idea behind generating functions, and ending with the basic concepts underlying Hamilton–Jacobi theory and action–angle variables. [Related videos] ∘ Playlist Classical Physics for Quantum Mechanics https://www.youtube.com/playlist?list=PL_UV-wQj1lvX-6uNvdvOHOopu4WZ_dE5w ∘ Playlist video series on Quantum Physics https://www.youtube.com/playlist?list=PL_UV-wQj1lvVxch-RPQIUOHX88eeNGzVH [References] ∘ A. Sommerfeld, "Mechanics: Lectures on Theoretical Physics, Vol. 1," 2nd edition (1952) ∘ M. Born, W. Heisenberg, and P. Jordan, "Zur Quantenmechanik II," Z. Phys. 35, 557 (1926) ∘ 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 ∘ W. R. Hamilton, "Second Essay on a general method in dynamics," Phil. Trans. R. Soc.125, 95 (1835) https://doi.org/10.1098/rstl.1835.0009 ∘ H. Goldstein et al., "Classical Mechanics," 3rd edition (2000) ∘ C. G. J. Jacobi, "Vorlesungen über Dynamik," Georg Reimer, Berlin (1866) ∘ C. G. J. Jacobi, "Über die Reduction der Integration der partiellen Differentialgleichungen erster Ordnung zwischen irgend einer Zahl Variabeln auf die Integration eines einzigen Systemes gewöhnlicher Differentialgleichungen," J. Reine Angew. Math. 17, 97–162 (1837) [Credits] Solar system, by Orrery under CC BY-SA 4.0 Animated mass spring by Svjo under CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/deed.en Ocean waves by J. Cheney, free use on Pexels https://www.pexels.com/video/ocean-waves-3586676/ Soothing ocean waves sound by Dragon Studio, free use on Pixabay https://pixabay.com/sound-effects/nature-soothing-ocean-waves-372489/