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Three-Dimensional Direct Scattering Theory-Chapter 2.1.2

Elsevier Ltd
DOI: 10.1016/b978-012613760-6/50035-8


Publisher Summary This chapter discusses the tools for the calculation of the differential cross section of elastic potential scattering and its properties, either for single particles subject to a given potential V(x) or for pairs of particles in their centre-of-mass (c.m.) system whose mutual interaction is described by V(x). The Fourier transform (with respect to the time) Ψ(+) of the configuration-space wave function of this particle solve the time-independent Schrödinger equation. The functions Ψ(+) , together with the bound-state eigenfunctions form a complete set on L2(R3) in the sense of generalized Fourier integrals. The high-energy behavior of the scattering amplitude depends critically on the scattering direction. In dispersion relation, its analog in optics expresses the frequency dependence of the real part of the index of refraction in terms of its imaginary part, i.e., of the absorption coefficient.

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