Use of harmonic inversion techniques in the periodic orbit quantization ofintegrable systems

Harmonic inversion has already been proven to be a powerful tool for the an alysis of quantum spectra and the periodic orbit orbit quantization of chao tic systems. The harmonic inversion technique circumvents the convergence p roblems of the periodic orbit sum and the uncertainty principle of the usua l Fourier analysis, thus yielding results of high resolution and high preci sion. Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized in this paper for the semiclassical quantization of integrable systems. Thus, harmonic invers ion is shown to be a universal tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: fir stly, the periodic orbit quantization will be extended to include higher or der h corrections to the periodic orbit sum. Secondly, the use of cross-cor related periodic orbit sums allows us to significantly reduce the required number of orbits for semiclassical quantization, i.e., to improve the effic iency of the semiclassical method. As a representative of regular systems, we choose the circle billiard, whose periodic orbits and quantum eigenvalue s can easily be obtained.