NONTRIVIAL ATTRACTORS IN A MODEL RELATED TO THE 3-BODY QUANTUM PROBLEM

A model of a quantum mechanical system related to the three-body probl em is studied. The model is defined in terms of a symmetric pseudo-dif ferential operator (PDO) with unbounded symbol. The entire family of s elf-adjoint extensions of this operator is studied using harmonic anal ysis. A regularization procedure for this PDO is introduced and the sp ectral properties of the operators obtained in this way are investigat ed. The limit behavior of the regularized operators when the regulariz ation parameter is removed is analyzed and a nontrivial attractor is e xhibited.