  We consider classical and quantum one and two-dimensional systems with ladder
operators that satisfy generalized Heisenberg algebras. In the classical case,
this construction is related to the existence of closed trajectories. In
particular, we apply these results to the infinite well and Morse potentials.
We discuss how the degeneracies of the permutation symmetry of quantum
two-dimensional systems can be explained using products of ladder operators.
These products satisfy interesting commutation relations. The two-dimensional
Morse quantum system is also related to a generalized two-dimensional Morse
supersymmetric model. Arithmetical or accidental degeneracies of such system
are shown to be associated to additional supersymmetry.
