The Discrete Spectrum States of Finite-Dimensional Quantum Systems Connected with Lie Algebras

Abstract

We consider the problem of finding the energy levels and wave functions of discrete-spectrum states for a class of Hamiltonians connected with root systems of the Lie algebras and in the limit case describing quantum systems of N interacting particles on a straight line in the Morse potential. It is shown that this problem may be reduced to an algebraic problem. Exact expressions are obtained for the dependence of energy levels on parameters of the interaction potential.