Exact Ground State of Some One-DimensionalN-Body Systems with Inverse ("Coulomb-Like") and Inverse-Square ("Centrifugal") Pair Potentials

We exhibit the exact ground state and the corresponding binding energy of the system composed of $N$ (nonidentical) quantum-mechanical particles interacting in one dimension via the potential $V_{\mathrm{ij}}(x_i-x_j)=g{(x_i-x_j)}^{-2\mathrm{}}+(f_i-f_j){(x_i-x_j)}^{-1\mathrm{}}$. We discuss some special choices of the constants $f_i$ and $g$ that yield examples of possible physical interest.