Hamiltonian formalism and the state of a physical system

The purpose of this paper is to trace in a brief and readable manner, the evolution of mechanics from Newton to quantum mechanics. The key to the transition is the Hamiltonian formalism. We produce Hamiltonʹs equations in special cases to give some sense of the importance and intrinsic interest in this formalism. Several examples are given to illustrate the power of the techniques. The idea of the “state” of a physical system is discussed and connections to quantum mechanics are made.