We present a geometrical approach to the inverse scattering problem for the Schrödinger and Klein-Gordon equations. For given scattering operator S we show uniqueness of the potential, we give explicit limits of the high-energy behavior of the scattering operator, and we give reconstruction formulas for the potential.
Our mathematical proofs closely follow physical intuition. A key observation is that at high energies translation of wave packets dominates over spreading during the interaction time.
Extended Abstract (17 pages) of our lectures at the
"First MaPhySto Workshop on Inverse Problems:
Inverse Problems in Stratified Media",
April 1999, Dept. Math. Sciences, Univ. of Aarhus, Denmark
to appear in the conference booklet.
Preprint available by anonymous ftp from
ftp.iram.rwth-aachen.de (134.130.161.65)
in the directory /pub/papers/enss/
as LaTeX2e file:
en-99-1.tex or
en-99-1.dvi or
Postscript
en-99-1.ps