diffusion coefficient, not the self diffusion coefficient[@phillies1974a; @phillies1974b]. Theoretical approaches to computing $g^{(1)}(q,t)$ and the mutual diffusion coefficient of non-dilute colloid solutions have historically followed routes very different from the routes that are based on the displacement distribution function $P(\Delta x, t)$. Only very recently[@phillies2012a] was a solution for $g^{(1)}(q,t)$ in terms of displacement distribution functions obtained. In this solution, the expansion of eq \[eq:g1qgeneral\] was shown to require averages over two different displacement distribution functions, namely $P(\Delta x, t)$ and a new distribution function $P_{2}(\Delta x, t, \mathbf{R}_{12})$. $P_{2}$ is a two-particle conditional displacement distribution function, in which $\Delta x$ is the displacement of particle $1$ during $(0, t)$ given that the vector $\mathbf{R}_{12}$ from particle $1$ to some particle $2$ at time $0$ has a given value.

Special Case: Probes in Simple Newtonian Liquids \[sectionsimple\] 
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The earliest quasielastic scattering experiments were performed on dilute suspensions of monodisperse scattering particles in simple Newtonian solvents. Cummins, et al.’s results on polystyrene spheres in water[@cummins1964a] are the archetype. The resulting spectra were interpreted by invoking a mechanical model for the motions of diffusing particles. The mechanical model was provided by the Langevin equation, which in one dimension is $$m\frac{d^{2} x(t) 