Application of Berry and Taborʹs trace formula to the 2D Fermi resonance Hamiltonian

The density of states is computed for the 2D Fermi resonance Hamiltonian using Berry and Taborʹs trace formula (or path integral quantization). As an example, the first 44 levels arising from combinations andovertones of the stretching and bending vibrations of CS2 are reproduced up to 5000 cm−. The three different kinds of ‘noise’ in the computed density of states, namely (i) high-frequency noise, (ii) large spurious peaks and (iii) the failure of the (i) the neglect of periodic orbits with periods larger than a given upper limit, (ii) EBK semiclassical levels lying at the boundary of the classically allowed region and having, therefore, no quantum counterpart and (iii) the failure of the stationary phase approximation to handle smoothly the entrance of periodic orbits in the classically allowed region. The intensity of the small spurious peaks is reduced when using a uniform trace formula. Introduction in the uniform trace formula of complex periodic orbits erases these small spurious peaks.