The Difference Between Hamiltonian and Quantum Mechanics

In newtonian mechanics, that line intercepts the one for hamiltonian mechanics. Hamiltonians work with quantum operators and can be quantized. Legrangian mechanics cannot always be quanized. And so we have these things called equations of motion but they don't explicitly tell you where the particle is and where it's going. It just tells you the rule that it must follow no matter where it is.