= Hartree product state
{c}
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 $\varphi$, the symmetric fixed-number form is $(a_\varphi^\dagger)^N|0\rangle/\sqrt{N!}$. 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.
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