Exactly soluble quantum mechanical and two-dimensional quantum field systems

The review deals with the study of one class of exactly integrable quantum dynamic systems. One-dimensional and two-dimensional systems, possessing a group of internal symmetries, are referred to the class. For one-dimensional generalized Todda chain the integration both in the Heisenberg and Schroedinger pictures is realized. In the corresponding two-dimensional tasks the Heisenberg field operators are obtained both in periodic and non-periodic case as to spatial coordinate. The methods developed are used to integrate quantum system, described by the Liouville supersymmetric equation