Quote by atyy
The Lagrangian is a way to get the Hamiltonian.

So
Lagrangian = position/velocity
Hamiltonian = position/momentum, potential
You mentioned the Lagrangian is a way to get the Hamiltonian, meaning the position/velocity is a way to get the position/momentum and potential? How come?
Sometimes it's easier to incorporate symmetries by using the Lagrangian.

Symmetries like U(1)? Why is it earlier in Lagrangian?
The Hamiltonian is still required because it generates "unitary" time evolution.

Why, there is no time in Lagrangian?
Roughly, unitarity is is what makes probabilities sum up correctly.

Probability can't occur in Lagrangian?