Some exact results for the many-body problem in one dimension with repulsive delta-function interaction

Abstract

The repulsive 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. © 1967 The American Physical Society.