If T (r elec , r hole ) is to serve as the excitonic wave function then it might seem that |T (r elec , r hole )| 2 should be the corresponding probability density, although this analogy breaks down when one realizes that the normalization condition in Eq. (4.6) is not generally obeyed for correlated wave functions. (This fact has occasionally been used to quantify deviation from one-particle character. ) For single-excitation wave functions, however, Eq. (4.6) is strictly valid and one may integrate over either r ≡ r elec or r ′ ≡ r hole to obtain separate one-particle densities for the electron and the hole. For TD-DFT, these quantities are the same as the particle and hole densities defined in Section 2.2. In terms of T (r elec , r hole ), they are ∆ρ elec (r elec ) = T (r elec , r hole ) 2 dr hole (5.1a) ∆ρ hole (r hole ) = T (r elec , r hole ) 2 dr elec .