Abstract
In this paper we give an elementary method to study an inverse scattering problem for a pair of Hamiltonians (H(h),
H0(h)) on L2
(IRn
), where H0(h) = - h
2 ∆, H(h) = H0(h) + V, and V is a short-range potential. We show that, in dimension
n 3, the scattering operators
( ); (0, ] S h h h0
which are localized near a fixed energy
0
,determine the
asymptotic of the potential V at infinity. This approach can be used to solve an inverse scattering problem for isotropic
external metrics.
H0(h)) on L2
(IRn
), where H0(h) = - h
2 ∆, H(h) = H0(h) + V, and V is a short-range potential. We show that, in dimension
n 3, the scattering operators
( ); (0, ] S h h h0
which are localized near a fixed energy
0
,determine the
asymptotic of the potential V at infinity. This approach can be used to solve an inverse scattering problem for isotropic
external metrics.