Suppose we have a system with M nuclei and N electrons(adsbygoogle = window.adsbygoogle || []).push({});

the electron density is defined as:

[itex]\rho(\mathbf{r}) = \sum\limits_{\sigma = \uparrow, \downarrow} \sum\limits_{i}^N \psi^{*}_{i}(\mathbf{r\sigma})\psi_{i}(\mathbf{r\sigma})

[/itex]

i would like to know if it is valid to express it in the following way

[itex]\rho(\mathbf{r}) = 2 \sum\limits_{i}^N \psi^{*}_{i}(\mathbf{r})\psi_{i}(\mathbf{r}) = 2 \sum\limits_{i}^N |\psi_{i}(\mathbf{r})|^{2}

[/itex]

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# Electron density expression

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