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I'd like to ask you about interpretation of electron density definition. According to the "Handbook of Molecular Physics and Quantum Chemistry" it goes like:

##\rho (\textbf{r})=N \sum_{\sigma_1}^{\sigma_N} \idotsint_{\mathbb{R^3}} |\psi_V (\textbf{r}_1, \sigma_1;\dots ;\textbf{r}_N,\sigma_N)|^2 d^3\textbf{r}_2 \dots d^3\textbf{r}_N##

I know that my question may be a little imprecise so please - be patient. I'd like to know how to iterpret this definition. Why in the integral is only ##d^3\textbf{r}_2 \dots d^3\textbf{r}_N## but no ##d^3\textbf{r}_1d^3\textbf{r}_2 \dots d^3\textbf{r}_N##. How to explain this equation using physical viewpoint and how to explain it methematically ?

Feel free to add any helpful information to understand this definition.

Thanks in advance.

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# Electron Density

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