Some Exact Results for the ManyBody Problem in one Dimension with Repulsive DeltaFunction Interaction
Abstract
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 S_{N}. 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 groundstate problem of spin 1/2 fermions is reduced to a generalized Fredholm equation.
 Publication:

Physical Review Letters
 Pub Date:
 December 1967
 DOI:
 10.1103/PhysRevLett.19.1312
 Bibcode:
 1967PhRvL..19.1312Y