Particular Integrability and (Quasi)-exact-solvability
  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. 
Alexander V. Turbiner
math-ph math.MP nlin.SI physics.class-ph quant-ph