Quantization of non-integrable Hamiltonian by periodic orbits: a case study of chaotic DCN vibration

The action integrals of periodic orbits of the non-integrable (chaotic) two-mode system of DCN stretch vibration were analyzed to show ample linear relations. This enables us to obtain by extrapolation all the action integrals of any periodic orbits and at any energies from very few arbitrary action integrals. Based on this property, a very simple and easy semiclassical quantization algorithm by numerical arithmetic was proposed for low excitation which is chaotic classically. The result shows less than 1% deviation from the exact quantal method.