Interacting fermions and bosons with definite total momentum

Any exact eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a symmetry-broken function $\Phi$. For two particles, we exactly express $\Phi$ in terms of (single-particle) orbitals for all energy levels and any interparticle interaction. Especially for the ground state, $\Phi$ is given by the simple Hartree-Fock and Hartree Ansätze for fermions and bosons, respectively. Implications for several and many particles as well as a numerical example for interacting bosons are provided.