Journal of Statistical Physics, Vol. 109, Nos. 5/6, December 2002. p. 1051-1072.
We show that in d >/ 2 dimensions the N-particle kinetic energy operator with periodic boundary conditions has symmetric eigenfunctions which vanish at particle encounters, and give a full description of these functions. In two and three dimensions they represent common eigenstates of bosonic Hamiltonians with any kind of contact interactions, and illustrate a partial ‘‘multi-dimensional Bethe Ansatz’’ or ‘‘quantum KAM theorem.’’..