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Are the electron density in density functional theory, ρ(r), and probability density, defined as wave function squared, the same quantities?

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In the Hartree approximation the electron density is computed as the sum of the probability densities of the occupied orbitals:

$$\rho=\sum_{j\;\mathrm{occupied}} \Psi_j(\vec{r})^*\Psi_j(\vec{r})$$

Source: Electronic Structure of Materials, A. Sutton

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