Quantum Poincare Section of a Two—Dimensional Hamiltonian in a Coherent State Representation

We study the quantum behaviour of a quasi-integrable Hamiltonian.The unperturbed Hamiltonian displays degeneracies of energy levels,which become avoided crossing under a nonintegrable perturbation.In this two-dimensional system,the quantum Poincare section plot is constructed in the coherent state representation with the restriction that the centres of the wavepackets are confined at thd classical surface of constant energy.It is found that the quantum Poincare section plot obtained in this way provides an evident counterpart of the classical system.