Exact solution of a many body problem with nearest and next-nearest neighbour interactions

Recently, a partially solvable many-body problem with nearest and next-near est neighbour interactions is proposed [1]. We show that by adding a suitab ly chosen momentum dependent nearest neighbour interaction, such a model ca n be converted into an integrable system with Lax operator formulation and related conserved quantities. We also solve the eigenvalue problem for the model exactly and as a byproduct obtain some identities involving associate d Laguerre polynomials. (C) 2001 Elsevier Science B.V. All rights reserved.