History of Lagrangian

	Revision 18 . . (edit) December 13, 2001 3:42 am by CYD
	Revision 17 . . (edit) December 13, 2001 3:40 am by CYD
	Revision 16 . . (edit) December 12, 2001 9:29 am by CYD
	Revision 15 . . (edit) December 11, 2001 5:23 am by CYD [* typo]
	Revision 14 . . December 10, 2001 8:06 pm by (logged).126.156.xxx [Corrected Feynman's link]
	Revision 13 . . December 10, 2001 8:05 pm by (logged).126.156.xxx
	Revision 12 . . (edit) December 10, 2001 5:38 pm by CYD [* some corrections]
	Revision 11 . . December 10, 2001 5:31 pm by CYD
	Revision 10 . . December 10, 2001 5:13 pm by CYD
	Revision 9 . . (edit) December 10, 2001 4:50 pm by CYD
	Revision 8 . . December 10, 2001 4:50 pm by CYD
	Revision 7 . . December 10, 2001 4:49 pm by CYD
	Revision 6 . . December 10, 2001 4:48 pm by CYD
	Revision 5 . . December 10, 2001 4:48 pm by CYD
	Revision 4 . . (edit) December 10, 2001 4:47 pm by CYD
	Revision 3 . . (edit) December 10, 2001 4:45 pm by CYD
	Revision 2 . . December 10, 2001 4:44 pm by CYD
	Revision 1 . . December 10, 2001 4:43 pm by CYD [* Start node on Lagrangian]

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Difference (from prior major revision) (minor diff, author diff)

Changed: 3c3

L = T - V

:L = T - V

Changed: 7c7

∂L/ ∂q = d/dt (∂ L/∂ q′ )

:∂L/ ∂q = d/dt (∂ L/∂ q′ )

Changed: 16c16

S = ∫ dt L

:S = ∫ dt L

Changed: 18c18

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.