their action. The action corresponding to the various paths is used to calculate the path integral, that gives the probability amplitudes of the various outcomes. Although equivalent in classical mechanics with Newton's laws, the action principle is better suited for generalizations and plays an important role in modern physics. Indeed, this principle is one of the great generalizations in physical science. In particular, it is fully appreciated and best understood within quantum mechanics. Richard Feynman's path integral formulation of quantum mechanics is based on a stationary-action principle, using path integrals. Maxwell's equations can be derived as conditions of stationary action. See also Analytical mechanics Configuration space Hamilton–Jacobi equation Phase space Geodesics as Hamiltonian flows References W.R. Hamilton, "On a General Method in Dynamics.", Philosophical Transactions of the Royal Society Part II (1834) pp. 247–308; Part I (1835) pp. 95–144. (From the collection Sir William Rowan Hamilton (1805–1865): Mathematical Papers edited by David R. Wilkins, School of Mathematics, Trinity College, Dublin 2, Ireland. (2000); also reviewed as On a General Method in Dynamics) Goldstein H. (1980) Classical Mechanics, 2nd ed., Addison Wesley, pp. 35–69. Landau LD and Lifshitz EM (1976) Mechanics, 3rd. ed., Pergamon Press. (hardcover) and (softcover), pp. 2–4. Arnold VI. (1989) Mathematical Methods of Classical Mechanics, 2nd ed., Springer Verlag, pp. 59–61. Cassel, Kevin W.: Variational Methods with Applications in Science and Engineering, Cambridge University Press, 2013. Lagrangian mechanics Calculus of variations Principles William Rowan Hamilton