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-nearest neighbour interactions is proposed [1]. We show that by adding a suitably chosen momentum dependent nearest neighbour interaction, such a model can 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 associated Laguerre polynomials. (C) 2001 Elsevier Science B.V. All rights reserved.