Dynamical quantities transfer probability

Whether the inactive region is a true continuum (e.g., photofragmentation) or a quasi-continuum comprised of an enormous density of rigorously bound eigenstates (polyatomic molecule dynamics, Section 9.4.14) is often of no detectable consequence. The dynamical quantities discussed in Section 9.1.4 (probability density, density matrix, autocorrelation function, survival probability, transfer probability, expectation values of coordinates and conjugate momenta) describe the active space dynamics without any reference to the detailed nature of the inactive space. 

The quantity 17(f) is the time-dependent friction kernel. It characterizes the dissipation effects of the solvent motion along the reaction coordinate. The dynamic solute-solvent interactions in the case of charge transfer are analogous to the transient solvation effects manifested in C(t) (see Section II). We assume that the underlying dynamics of the dielectric function for BA and other molecules are similar to the dynamics for the coumarins. Thus we quantify t](t) from the experimental C(t) values using the relationship discussed elsewhere [139], The solution to the GLE is in the form of p(z, t), the probability distribution function. 

For problems involving heavy-particle dynamics and in situations where appreciable averaging is involved, classical or semiclassical methods [3.12,13] often prove acceptable. For these problems it is often the case that classical mechanics provides a poor picture of the elementary aspects of the process (e.g., specific transition probabilities) while at the same time it gives a rather good estimate of more-averaged quantities (e.g., energy transfer). 

The experimentally measured quantity in a scattering experiment is the dynamic structure factor S(q, co), describing the probability for the photon to acquire a momentum transfer q = k — koandan energy transfer o) = )o — o). In 1954, Van Hove demonstrated that the dynamic structure factor, known as the scattering function, relates to the probability G (r, t) for finding any particle at position r and time t when the particle was at r = 0 and t = 0 before by a spatial and temporal Fourier transforms [89] ... 

---