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Feb11-12, 09:23 PM
P: 381
Quote Quote by TriTertButoxy View Post
The reason people talk about Lagrangians in QFT is because theories are expressed Lorentz-invariantly using the Lagrangian, but not using the Hamiltonian (since the Hamiltonian is an energy which depends on the Lorentz frame).
In short. Lagrangians don't have to involve forces or potential while Hamiltonians do. But I heard you can introduce forces in Lagrangians too, how?

In QM, the Hamiltonian is more useful since many problems involve, in some form or other, diagonalizing the Hamiltonian operator (i.e. solving the Schrodinger eqn). This is much more tractable due to fact that most often, the number of degrees of freedom are much fewer than that of QFT.
This is due to the fact that Schrodinger equation solves for potentials and involves energy so Hamiltonian is used and in my original message I mentioned Hamiltonian solves for potential.. so this point is correct.