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Inverse Scattering at Fixed Energy

In: Mathematical Physics X

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  • Adrian I. Nachman

    (University of Rochester, Department of Mathematics)

Abstract

Let - Δ + V be a quantum mechanical two-body Hamiltonian in L 2(R n ), n ≥ 3, and let S(k) be the corresponding scattering matrix at energy k 2. We consider the classical problem of recovering V from knowledge of S(k) at one energy. The potential V(x) is not assumed to have any spherical symmetry. (The spherically symmetric case, including the non-uniqueness which arises if one allows potentials with reasonably mild decay at infinity, has been extensively studied—see [3] and references given there.) We show (Theorem 3.1) that if V has compact support and is in L n/2 then it is uniquely determined by S(k); the proof gives a method to reconstruct the potential from the scattering matrix.

Suggested Citation

  • Adrian I. Nachman, 1992. "Inverse Scattering at Fixed Energy," Springer Books, in: Konrad Schmüdgen (ed.), Mathematical Physics X, pages 434-441, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-77303-7_48
    DOI: 10.1007/978-3-642-77303-7_48
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