 Hartree product state

A many-particle trial state built from one-particle factors, without the additional correlations of a general many-body wavefunction. For identical bosons occupying one normalized orbital $\phi$, the symmetric fixed-number form is $(a_{\phi }^{†}{)}^N|0⟩/\sqrt{N!}$. Its field expectation is zero because annihilation changes particle number, while its one-body density matrix has the macroscopic eigenvalue $N$. An antisymmetrized multi-orbital fermionic trial state instead belongs to the Hartree-Fock construction.