Ehrenfest's Theorem
From QED
If is an operator with no explicit time dependence, then
Ehrenfest's Theorem describes the time evolution of the expected value of dynamic variables. The relations that derive from this system share a striking similarity to the relations of classical physics. For the majority of systems, as the size of the system increases the relative fluctuations decrease, and so the systems begin to resemble, more and more, their classical counterparts.
By the product rule
By the Schrödinger Equation
Finally
Note the striking similarity to the classical equation, written in terms of Poisson Brackets.
This page was recovered in October 2009 from the Plasmagicians page on Ehrenfest's_Theorem dated 19:53, 6 December 2006.