Underdetermined systems of partial differential equations (Q2738194)

The authors consider the classical and quantum-mechanical equations of motion for a system with a Lie-Poisson structure, i.e., where the fundamental Poisson brackets or the commutation relations, resp., are derived from the structure constants of a finite-dimensional Lie algebra. Using a power series ansatz this leads to a sequence of underdetermined systems of partial differential equations whose solution spaces are parametrised by the Hamiltonian. As illustrative examples the Lie algebras of SU(2) and \(E_2\) and the Heisenberg algebra are considered.