The electron probability distribution function, \(\rho \), defined as \[\rho (\mathbf{r}) = n\ \int \Psi ^{\rm{*}}\left[\mathbf{r}(1),\mathbf{r}(2)\,\rm{...}\,\mathbf{r}(n)\right]\ \Psi \left[\mathbf{r}(1),\mathbf{r}(2)\,\rm{...}\,\mathbf{r}(n)\right]\rm{d}\mathbf{r}(2)\,\rm{...}\,\rm{d}\mathbf{r}(n)\] where \(\Psi \) is an electronic wave-function and integration is made over the coordinates of all but the first electron of \(n\). The physical interpretation of the electron density function is that \(\rho \ \mathrm{d}\mathbf{\mathbf{r}}\) gives the probability of finding an electron in a volume element \(\mathrm{d}\mathbf{\mathbf{r}}\), i.e., electron density in this volume.