This is goosebump material! It is fascinating how concepts from classical mechanics port over into quantum mechanics. If we'd stuck with F=ma, perhaps we may n

This is goosebump material! It is fascinating how concepts from classical mechanics port over into quantum mechanics. If we'd stuck with F=ma, perhaps we may not have gone far. However, the Hamiltonian and Lagrangian approaches are sweet ports. Noether's theorem [1] connects symmetries of a lagrangian with corresponding conservation laws. Time translation symmetry implies energy conservation. Space translation symmetry implies momentum conservation in the direction of translation. This ports directly to QM. Feynman, in his lecture series, mentions another such symmetry - phase translation symmetry - that exists for QM actions and asks what conservation law does that correspond to. It is the conservation of charge. Mind blown! [1]: https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem