Hamilton’s crowning achievement was deriving both Lagrangian mechanics and Hamiltonian mechanics, directly in terms of a general form of his principle of least action S.
In two papers published in 1834 and 1835, Hamilton announced a dynamical principle upon which it is possible to base all of mechanics, and indeed most of classical physics. Hamilton was seeking a theo...In two papers published in 1834 and 1835, Hamilton announced a dynamical principle upon which it is possible to base all of mechanics, and indeed most of classical physics. Hamilton was seeking a theory of optics when he developed Hamilton’s Principle, plus the field of Hamiltonian mechanics. Hamilton’s Principle can be considered to be the fundamental postulate of classical mechanics. It replaces Newton’s postulated three laws of motion.
In quantum mechanics, such as the motion of an electron in an atom, we know that the particle does not follow a well-defined path, in contrast to classical mechanics. Where does the crossover to a wel...In quantum mechanics, such as the motion of an electron in an atom, we know that the particle does not follow a well-defined path, in contrast to classical mechanics. Where does the crossover to a well-defined path take place? Feynman (in Feynman and Hibbs) gives a nice picture to help think about summing over paths.
