Let q0 and q1 be the position at respective initial and final times t0 and t1. Using the [calculus of variations]?, it can be shown that the Euler-Lagrange equation is equivalent to the statement that the system undergoes the trajectory between t0 and t0 that minimizes the action. This is known as the Principle of Least Action, and written as
Let q0 and q1 be the position at respective initial and final times t0 and t1. Using the [calculus of variations]?, it can be shown that the Euler-Lagrange equation is equivalent to the statement that the system undergoes the trajectory between t0 and t1 that minimizes the action. This is known as the Principle of Least Action, and written as
Changed: 20c20
δ S = 0
:δ S = 0
Changed: 24c24
Feynman's path integral formulation extends the Principle of Least Action to quantum mechanics. In this formulation, particles travel every possible path between the initial and final states; the probability of a specific final state is obtained by summing over all possible trajectories leading to it. This point of view is influential in modern particle physics, and underlies much of quantum field theory.
Feynman's [path integral formulation]? extends the Principle of Least Action to quantum mechanics. In this formulation, particles travel every possible path between the initial and final states; the probability of a specific final state is obtained by summing over all possible trajectories leading to it. This point of view is influential in modern particle physics, and underlies much of quantum field theory.