ABSTRACT
In general, the expectation values of observable quantities depend on time. In quantum mechanics, these values are given by the expression:
< X >t=< A(t)|X(t)|A(t) >. (10.1)
There is an intrinsic ambiguity in determining the time dependence on the various elements (bra, ket and operator) which comprise the right hand side of equation (10.1) because we can transfer this dependence from one element to another, while keeping unchanged the expectation value < X >t, which is all we can measure on the system. The ambiguity gives rise to different descriptions of the motion, connected to unitary time-dependent transformations, thus equivalent to each other. In the following sections, we describe the Schro¨dinger and Heisenberg representations. Subsequently we will introduce a third description of the motion or interactions: the Dirac representation, also called the interaction representation, which is particularly useful in the case of weakly interacting systems.
