- #1
arierreF
- 79
- 0
Suppose we have a system with M nuclei and N electrons
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]
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]