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A multidimensional inverse-scattering method. (English) Zbl 0557.35032

Summary: A formal solution of the inverse scattering problem for the n-dimensional time-dependent and time-independent Schrödinger equations is given. Equations are found for reconstructing the potential from scattering data purely by quadratures. The solution also helps elucidate the problem of characterizing admissible scattering data.

MSC:

35J10 Schrödinger operator, Schrödinger equation
35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
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