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Titlebook: Inverse Problems in Scattering; An Introduction G. M. L. Gladwell Book 1993 Springer Science+Business Media Dordrecht 1993 Potential.algori

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书目名称Inverse Problems in Scattering
副标题An Introduction
编辑G. M. L. Gladwell
视频videohttp://file.papertrans.cn/475/474699/474699.mp4
丛书名称Solid Mechanics and Its Applications
图书封面Titlebook: Inverse Problems in Scattering; An Introduction G. M. L. Gladwell Book 1993 Springer Science+Business Media Dordrecht 1993 Potential.algori
描述.Inverse Problems in Scattering. exposes some of themathematics which has been developed in attempts to solve theone-dimensional inverse scattering problem. Layered media are treatedin Chapters 1--6 and quantum mechanical models in Chapters 7--10.Thus, Chapters 2 and 6 show the connections between matrix theory,Schur‘s lemma in complex analysis, the Levinson--Durbin algorithm,filter theory, moment problems and orthogonal polynomials. Thechapters devoted to the simplest inverse scattering problems inquantum mechanics show how the Gel‘fand--Levitan and Marchenkoequations arose. The introduction to this problem is an excursionthrough the inverse problem related to a finite difference version ofSchrödinger‘s equation. One of the basic problems in inversequantum scattering is to determine what conditions must be imposed onthe scattering data to ensure that they correspond to a regularpotential, which involves Lebesque integrable functions, which areintroduced in Chapter 9..
出版日期Book 1993
关键词Potential; algorithms; complex analysis; inverse scattering problem; mathematics; mechanics; quantum mecha
版次1
doihttps://doi.org/10.1007/978-94-011-2046-3
isbn_softcover978-0-7923-2478-2
isbn_ebook978-94-011-2046-3Series ISSN 0925-0042 Series E-ISSN 2214-7764
issn_series 0925-0042
copyrightSpringer Science+Business Media Dordrecht 1993
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The Inversion of Discrete Systems Using Non-Causal Solutions,in Chapter 2 the crucial property of causal solutions that was used ..This states that at time . the disturbance which started at the surface ξ= 0 has just reachedξ= ., and nothing has had time to come up from below to reachξ= . in other words, there is just a down-wave, no up-wave.
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,The Schrödinger Equation on the Half Line,the enumerable spectrum is actually finite. We introduce three solutions of Schrödinger’s equation: the regular solution, the Jost solution, and the wave solution. We show how they are related to each other and to the Jost function. We will find that the Jost solution holds the key to the solution of the inverse problem considered in Chapter 10.
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The Lebesque Integral,ata 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’ . so that we can establish a one-to-one relationship between a class of possible potentials . and a class of possible scattering data.
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Some Simple Wave Phenomena, waves travel to our radio receiver as electromagnetic waves. Our radio receives these and converts them to electrical and then to sound waves which travel to our ear. They excite our ear drums which then send electrical signals to our brain. We ‘hear’ music!
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https://doi.org/10.1007/978-94-011-2046-3Potential; algorithms; complex analysis; inverse scattering problem; mathematics; mechanics; quantum mecha
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Solid Mechanics and Its Applicationshttp://image.papertrans.cn/i/image/474699.jpg
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