Particular Integrability and (Quasi)-exact-solvability

Alexander V. Turbiner

Published 2012-06-13, updated 2012-08-07Version 2

A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland Hamiltonians for all roots are found. In the classical case some special trajectories for which the corresponding particular constants of motion appear are indicated.