Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation (Q1582866)

The authors elaborate a quantum analogue of the procedure of reducing a classical Hamiltonian system to the orbits of the coadjoint representation of a Lie algebra. It is applied to quantum systems described by a linear partial differential equation. The method of noncommutative integration is involved into the construction. The procedure is illustrated on two systems (Goryachev-Chaplygin hydrostat and Kovalevskaya gyroscope) that cannot be integrated by separation of variables.