Bosonic coincidence enhancement in two orthogonal orbitals (source code)

= Bosonic coincidence enhancement in two orthogonal orbitals
{title2=$P_B(\mathbf r,\mathbf r)=2P_D(\mathbf r,\mathbf r)$}

Place one noninteracting spin-zero <boson> in each of two orthonormal orbitals $a,b$. Its normalized symmetric spatial <wavefunction> is $[a(\mathbf r_1)b(\mathbf r_2)+b(\mathbf r_1)a(\mathbf r_2)]/\sqrt2$. 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.