QUANTUM SURFACES OF SECTION FOR THE DIAMAGNETIC HYDROGEN-ATOM - HUSIMI FUNCTIONS VERSUS WIGNER FUNCTIONS

We compare quantum phase space distributions of individual quantum sta tes of the diamagnetic hydrogen atom obtained by means of Wigner funct ions with those given by Husimi functions. The comparison is carried o ut at effective hBAR approximately 0.035 and at a fixed scaled energy (epsilon = -0.316) which corresponds to an especially interesting mixe d classical phase-space structure. The object of the comparison is to establish which of the two distributions best correlates with the clas sical Poincare surface of section for a representative set of single s tates. As expected, the states investigated display the strongest posi tive intensity on a single local invariant phase-space structure (such as a scar or torus) and at this level there is little difference betw een the Husimi and the Wigner function. However the weak structures (f ringes of the Wigner function or zeros of the Husimi function) are sho wn here to be radically different for the Wigner relative to the Husim i representation. In both cases the weak structures permeate all of ph ase space. In addition they show different character for integrable an d chaotic dynamics and so reflect the global structure of phase-space to a much greater extent than the localized strong structure. The Wign er functions of selected states are shown to have additional dynamical ly significant structures which are not apparent in the Husimi functio ns. These include negative intensity features seen in the Wigner-but n ot the Husimi-functions which are very well correlated with structures of the classical Poincare surfaces of section. Despite its complex os cillatory nature the Wigner function delineates better classical featu res, for example showing the outline of islands of stability avoided b y states supported by chaotic regions with greater sharpness than the Husimi function.