Equations of Motion for Resonance Operators

An enormous amount of dynamical information is encoded in the I (r, R, t) that arises from any non-eigenstate preparation of a molecular system at t = 0. One way of displaying intelligible portions of this information is to plot, versus time, the expectation values of various coordinates and momenta, as discussed in Section 9.1.7. There are, however, other kinds of equations of motion. 

There are several standard results from time-dependent quantum mechanics that will prove useful. The equation of motion of the expectation value of any operator, O, 

This equation is especially useful when H can be written as a sum of simpler operators 

The system of coupled differential equations embodied in Eq. (9.1.87) describes the dynamics of the system in a numerically explicit but mechanistically opaque manner. A mechanism is a short list of the dynamically most important 

Energy may be viewed as flowing between Ediag and Eres. The cause of this energy flow may be traced to specific additive terms in Hres, 

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