Question: Determine the self-diffusion term in the dynamical structure factor (S_{text {self }}(boldsymbol{k}, omega)) in equation (15.6.41b) for the case of a single particle that diffuses

Determine the self-diffusion term in the dynamical structure factor $S_{\text {self }}(\boldsymbol{k}, \omega)$ in equation (15.6.41b) for the case of a single particle that diffuses according to the diffusion equation. Assume the process to be Gaussian for which $\left\langle e^{f}\rightangle=\exp \left(\left\langle f^{2} / 2\rightangle\right)$.

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