Bosonic coincidence enhancement in two orthogonal orbitals ($P_B(\mathbf{r},\mathbf{r})=2P_D(\mathbf{r},\mathbf{r})$)

Place one noninteracting spin-zero boson in each of two orthonormal orbitals $a,b$. Its normalized symmetric spatial wavefunction is $[a({\mathbf{r}}_1)b({\mathbf{r}}_2)+b({\mathbf{r}}_1)a({\mathbf{r}}_2)]/\sqrt{2}$. At coincident positions the probability density is $2|a(\mathbf{r}){|}^2|b(\mathbf{r}){|}^2$, twice the labelled distinguishable-product value. Coincidence at an exact point is understood as a density or the limit of small detector volumes. If both particles occupy the same orbital, the normalized product is already symmetric and this comparison gives factor one instead; the factor two is not a universal property of every two-boson state.