Guerin C.A
One-dimensional quantum scattering for potentials defined as measures
(71K, DVI file)

ABSTRACT.  We generalize the basic one-dimensional  scattering formalism 
to potentials defined as measures and retrieve the classical results that hold 
for smooth potentials. We introduce a set of generalized eigenfunctions for the 
corresponding Schr{\" o}dinger operator and study their analytical properties. 
This allows a characterization of the spectrum and an eigenfunction expansion. 
We also prove the existence and completeness of the wave operators and give
 explicit formulae for these latter.