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→The structure factor: added clarity about the intention of obtaining an averaged observable Tags: Mobile edit Mobile web edit |
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We can formally count these particles via <math> \sum_{i \neq 0} \delta ( \mathbf{r} - \mathbf{r}_i) </math>.
Taking the average we arrive at the expression <math>\textstyle \mathrm{d} n (\mathbf{r}) = \langle \sum_{i \neq 0} \delta ( \mathbf{r} - \mathbf{r}_i) \rangle</math>, with <math>\textstyle \langle \cdot \rangle</math> the ensemble average, yielding:
{{NumBlk|:| <math>g(\mathbf{r}) = \frac{1}{\rho} \langle \sum_{i \neq 0} \delta ( \mathbf{r} - \mathbf{r}_i) \rangle = V \frac{N-1}{N} \left \langle \delta ( \mathbf{r} - \mathbf{r}_1) \right \rangle</math>|{{EquationRef|5}}}}
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