Observables and Operators
The version of classical mechanics based on forces and Newton’s laws resists any meaningful reformation into a quantum theory because it depends critically on such concepts (trajectory, acceleration, etc.) that do not correspond to any observable reality in the quantum world. More productive for finding links between classical and quantum realms is an alternative formulation, where energy rather than force takes the central role. There are two essential elements in this formulation of classical mechanics. One is the idea of canonical coordinates in the so-called phase space (as opposed to regular three-dimensional configuration space), and the other is the concept of Hamiltonian.