Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group SN. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-{} fermions is reduced to a generalized Fredholm equation.