I will discuss the ground state and spectrum of excitations of a gaseous cloud in 1D. The goal is to promote a simple single-particle equation, which is employed to show the existence of quantum droplets in 1D. The substantial part of this talk will be devoted to recall the typical methods applied to study interacting slow bosons: a) ab initio many-body calculation (usually limited to a small number of atoms), b) single-body equations, e. g. Gross-Pitaevskii equation (very approximated). Firstly, I will remind these two viewpoints, and correspondence between them, on the well-understood case of atoms interacting via short-range potential. Interestingly, the simple single-body picture can be still useful even in the regimes of strong correlations. Then I will continue to non-local interactions, and present our understanding of ground state having properties of quantum droplets.
 W. Golletz, W. Górecki, R. Ołdziejewski, K. Pawłowski, Phys. Rev. Research 2, 033368 (2020)
 R. Ołdziejewski, W. Górecki, K. Pawłowski, K. Rzążewski, Phys. Rev. Lett. 124, 090401 (2020)