Given the Hamiltonian in QM pushes the state through time, and the Lagrangian is also an energy (therefore, in QM at least, should also evolve something through time, I think?), can we consider the Lagrangian being the evolution of the state function in some lower-energy view? Like maybe the particle's rest frame, rather than something fixed and more global?
I never was able to get a feel for the action in classical mechanics, other than it was formally true and made solving a lot of wacky problems way easier. So thanks for the pointer to the Hamilton-Jacobi equation. I like that Schrödinger's equation can sorta be viewed as the diffusion equation with a phase tossed in, so it's interesting and surprising that there's an analogue in classical mechanics. (Maybe I was absent from class that day.)
Dan Piponi (npub1x78…xn0m) Bartosz Milewski (npub1glg…tqzy)
Ray Lee
npub1fj…xjlf5
2025-05-03 23:03:24 UTC
in reply to nevent1q…suw9
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"content": "Given the Hamiltonian in QM pushes the state through time, and the Lagrangian is also an energy (therefore, in QM at least, should also evolve something through time, I think?), can we consider the Lagrangian being the evolution of the state function in some lower-energy view? Like maybe the particle's rest frame, rather than something fixed and more global?\n\nI never was able to get a feel for the action in classical mechanics, other than it was formally true and made solving a lot of wacky problems way easier. So thanks for the pointer to the Hamilton-Jacobi equation. I like that Schrödinger's equation can sorta be viewed as the diffusion equation with a phase tossed in, so it's interesting and surprising that there's an analogue in classical mechanics. (Maybe I was absent from class that day.)\n\n nostr:npub1x78ms56a50yyrl0t6ztxuksk70fp6n5c3wf9u3cl9k8a7g696t5s9nxn0m nostr:npub1glgxnwfzwxpvj3l6d96vxttum7rkfav3dmcwdkyqz9eqkt83mdfsaxtqzy",
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