Classical and quantum Liouville integrability of nonlinear Heisenberg equations Original Research Article

In classical theory a surprising result has long been derived that for the integrability of 2M2M Hamilton canonical equations MM invariants suffice. In quantum theory a similar situation is rather transparent due to the essential linearity of the theory. But in the most interesting problems the vanishing of commutators of invariants does not suffice for separation of new degrees of freedom unfortunately. We demonstrate the connection between the expansions of solutions in Fock states and those in normally ordered products of creation and annihilation operators for simple problems of quantum optics.