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Marchenko equation : ウィキペディア英語版
Marchenko equation
In mathematical physics, more specific in the one-dimensional inverse scattering problem, the Marchenko equation, named after Vladimir Marchenko, is derived by computing the Fourier transform of the scattering relation:
:
K(r,r^\prime) + g(r,r^\prime) + \int_r^ K(r,r^) g(r^,r^\prime) \mathrmr^ = 0

where
:g(r,r^\prime)\,
is a symmetric kernel, so that
:g(r,r^\prime)=g(r^\prime,r),\,
which is computed from the scattering data. Solving the Marchenko equation one obtains the kernel of the transformation operator K(r,r^\prime) from which the potential can be read off.
This equation is derived from the Gel'fand-Levitan integral equation, using the Povzner-Levitan representation.
==References==

* .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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