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knzhou
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Why not use the Lagrangian, instead of the Hamiltonian, in nonrelativistic QM?

Undergraduate classical mechanics introduces both Lagrangians and Hamiltonians, while undergrad quantum mechanics seems to only use the Hamiltonian. But particle physics, and more generally quantum field theory seem to only use the Lagrangian, e.g. you hear about the Klein-Gordan Lagrangian, Dirac Lagrangian, Standard Model Lagrangian and so on.

Why is there a mismatch here? Why does it seem like only Hamiltonians are used in undergraduate quantum mechanics, but only Lagrangains are used in quantum field theory?

Revo
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