The Determination of the Scattering Potential From the Spectral Measure Function, Vol. 3: Calculation of the Scattering Potential From the Scattering ... Schrödinger Equation (Classic Reprint) - Tapa dura

Sinopsis

Excerpt from The Determination of the Scattering Potential From the Spectral Measure Function, Vol. 3: Calculation of the Scattering Potential From the Scattering Operator for the One-Dimensional Schrödinger Equation

Several writers [3-1 have recently discussed the problem of obtaining the scattering potential from the scattering phases for a variety of radial wave equations. Their work is characterized by the fact that they require the per turbed eigenfunctions to approach the unperturbed eigenfunctions at the origin. From this boundary condition and from Specific properties of the unperturbed Hamiltonians and of the perturbation, they then Obtain the Gelfand - Levitan equa tionl In the special cases discussed in [l], [3] this equation was used to obtain the scattering potential in terms of the spectral measure function. By showing how the spectral measure function can be obtained from the scattering phases, it is then possible to derive the potential in terms of the phases.

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