CLOSED TRAJECTORIES AND 2-DIMENSIONAL TORI IN THE QUANTUM PROBLEM FORA 3-DIMENSIONAL RESONANT ANHARMONIC-OSCILLATOR

The classical and quantum problems for a three-dimensional anharmonic oscillator with V = )+(wm(2))(2)x(2)(2))+Omega(2)(x(1),x(2))x(3)(2))/2 are considered. The possibility of associating closed trajectories an d two-dimensional Invariant tori of the classical Hamiltonian system w ith asymptotic eigenfunctions and eigenvalues of the corresponding Sch rodinger operator, using the complex WKB method (and the complex Maslo v canonical operator) is analyzed.