Uniform semiclassical quantization of regular and chaotic classical dynamics on the Hénon–Heiles surfacea)

Abstract

Qualitative arguments (made substantially more quantitative in the accompanying article by Shirts and Reinhardt) are put forward which indicate that the apparently chaotic dynamics on the Hénon–Heiles surface display sufficient regularity on a short to intermediate (but not long) time scale to allow use of standard EBK quantization techniques, taking advantage of the remnants of manifold structure that these remarks imply. A complete uniform semiclassical quantization is carried out using the time independent technique of the Birkhoff–Gustavson normal form, recently introduced in the context of semiclassical quantization by Swimm and Delos.