IMPROVED SEMICLASSICAL QUANTIZATION OF SYSTEMS WITH A FEW DEGREES OF FREEDOM

The Birkhoff-Gustavson (BG) procedure for the reduction of a classical Hamiltonian to normal forms is used in the semiclassical quantization of systems with a few degrees of freedom. We argue that the use of a modified Hamiltonian, in which the actual potential is replaced by a potential constructed from the ground-state wave function, leads to an improvement of the quantization recipe for the excited states. The possibilities of the improved scheme axe enhanced in two ways: i) low-lying states may be described, and ii) potentials, for which the traditional BG procedure is not applicable, may be considered. The advantages of the method are illustrated in the quantization of a model linear triatomic molecule with (nonphysical) quartic and sextic anharmonicities.