It would be nice to have 3 videos in succession. One on Legendre transforms and their use in physics (thermodynamics etc), introducing action angle variables and the Hamilton Jacobi systems, and then finally moving onto Schrödinger's equation and how he derived
1 month ago
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@IsomorphicToIntingersAdjoin_i
I would like to see more pure mathematics on your channel .
1 month ago
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Both why not in a series of videos, but if you have to prioritize I would love to watch the Legendre transform in thermodynamics and optimization (I heard of it being used in this field)
1 month ago
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About arriving at the Schrödinger equation. Resnick and Eisberg, in their book 'Quantum physics' offer an interesting line of reasoning to arrive at the Schrödinger equation. Quoting the 4 constraints that Resnick and Eisberg set up: 1. Must be consistent with the de Broglie-Einstein relations 2. The sum of kinetic energy and potential energy must be a conserved quantity 3. The equation must be a linear equation; as in: given two solutions: an arbitray linear combination of those two must also be a solution. 4. Without presence of a potential the solutions must be sinusoidal traveling waves of constant wavelength and frequency. In the Resnick & Eisberg plausibility argument there is a direct connection from the de Broglie-Einstein relations to how the Schrödinger equation is different from the wave equation for classical mechanics. An April 2022 video that presents the Resnick & Eisberg plausibility argument: https://youtu.be/2WPA1L9uJqo?t=642 The exposition of the Resnick & Eisberg plausibility argument is about 18 minutes, the rest of the video discusses application of the Schrödinger equation. If you are interested, I transcribed the part of the Resnick & Eisberg book with the plausibility argument, if you contact me I'll be happy to provide it to you. As far as I'm aware of the Hamilton-Jacobi is quite an unknown equation. I know the name, but I don't know the form and I don't know what it does. It's not clear to me whether in the history of physics the Hamilton-Jacobi was ever used.
1 month ago
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Could explain in the future a good insight of what actually is "action" in physics? That's a really tough one to understand... Haha
1 month ago
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Abide By Reason
Hope you've enjoyed the last 2 videos on Lagrangian and Hamiltonian Mechanics! What would you like to see next? Feel free to comment other ideas below too.
1 month ago | [YT] | 40