Interaction picture as any other operator. In particular, let and be the density matrices in the interaction picture and the Schrödinger picture respectively. If there is probability to be in the physical state |"ψ"〉, then Transforming the Schrödinger equation into the interaction picture gives which states that in the interaction picture, a quantum state is evolved by the interaction part of the Hamiltonian as expressed in the interaction picture. If the operator "A" is time-independent (i.e., does not have "explicit time dependence"; see above), then the corresponding time evolution for "A"("t") is given by In the interaction picture the operators evolve in
Action (physics) (see also below). The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. This simple principle provides deep insights into physics, and is an important concept in modern theoretical physics. "Action" was defined in several now obsolete ways during the development of the concept. Expressed in mathematical language, using the calculus of variations, the evolution of a physical system (i.e., how the system actually progresses from one state to another) corresponds to a stationary point (usually, a minimum) of the action. Several different definitions