Serge Richard
Spectral and Scattering Theory for Schrodinger Operators with Cartesian Anisotropy
(812K, PostScript)

ABSTRACT.  We study the spectral and scattering theory of some n-dimensional 
anisotropic Schrodinger operators. The characteristic of the potentials 
is that they admit limits at infinity separately for each variable. We 
give a detailed analysis of the spectrum: the essential spectrum, 
the thresholds, a Mourre estimate, a limiting absorption principle and 
the absence of singularly continuous spectrum. Then the asymptotic 
completeness is proved and a precise description of the asymptotic 
states is obtained in terms of a suitable family of asymptotic 
operators.