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We completely solve the problem of classifying all one-dimensional quantumpotentials with nearest- and next-to-nearest-neighbors interactions whoseground state is Jastrow-like, i.e., of Jastrow type but depending only ondifferences of consecutive particles. In particular, we show that these modelsmust necessarily contain a three-body interaction term, as was the case withall previously known examples. We discuss several particular instances of thegeneral solution, including a new hyperbolic potential and a model withelliptic interactions which reduces to the known rational and trigonometricones in appropriate limits.

Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions