Convergence of model Heisenberg dynamics

The exactly solvable part of the Heisenberg algebra is found. It is shown that under the influence of a dynamics that approximates the Heisenberg dynamics an arbitrary potential in a certain class of potentials converges as $t\to\infty$ to a first integral of the model, while the initial state converges to a limit state. The actual dynamics corresponding to the exactly solvable part of the Heisenberg algebra is calculated exactly.