Derive equation (13.1.9) for hard spheres in one dimension from equation (13.1.7). Plot the pair correlation function

Question:

Derive equation (13.1.9) for hard spheres in one dimension from equation (13.1.7). Plot the pair correlation function for $n D=0.25,0.50,0.75$, and 0.90 . Determine the structure factor $S(k)$ numerically and plot it for the same densities. Compare your results with equation (13.1.21).

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