Quantum Poincaré 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-crossings under a nonintegrable perturbation. In this two-dimensional system, the quantum Poincaré section plot is constructed in the coherent state representation with the restriction that the centers of wavepackets are confined at the classical surface of constant energy. It is found that the quantum Poincaré section plot obtained in this way provides an evident counterpart of the classical system.