Abstract
One of the chief complications of the inverse scattering problem, for the Schrödinger equation or other more difficult equations, is the problem of assigning classes to the functions q(x) on the one hand, and the scattering data on the other, so that if q(x) belongs to the one class, then the scattering data will belong to the other, and vice versa. The most mathematically satisfying way of achieving this is to introduce the concept of Lebesgue integration. This allows us to widen the class of ‘functions’ q(x) so that we can establish a one-to-one relationship between a class of possible potentials q(x) and a class of possible scattering data.
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To be thus is nothing; but to be safely thus.
Macbeth. Act III,Scene 1.
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© 1993 Springer Science+Business Media Dordrecht
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Gladwell, G.M.L. (1993). The Lebesque Integral. In: Inverse Problems in Scattering. Solid Mechanics and its Applications, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2046-3_9
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DOI: https://doi.org/10.1007/978-94-011-2046-3_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4906-1
Online ISBN: 978-94-011-2046-3
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