Solution of the Inverse Scattering Problem for the Three - Dimensional Schrodinger Equation Using a Fredholm Integral Equation
نویسنده
چکیده
It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem is also clarified, and it is shown that the Fredholm integral equation is uniquely solvable if and only if the Riemann-Hilbert problem is uniquely solvable. Key words, inverse scattering, three-dimensional SchrSdinger equation, Fredholm integral equation AMS(MOS) subject classifications. 81U40, 35P25, 35Q15, 35R30, 47A40
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