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The semiclassical limit of quantum dynamics. II: Scattering theory. (English) Zbl 0666.35071
[For part I see J. Math. Phys. 29, No.2, 412-419 (1988; Zbl 0647.46060).]
We study the \(\hslash \to 0\) limit of the quantum scattering determined by the Hamiltonian \(H(\hslash)=-(\hslash^ 2/2m)\Delta +V\) on \(L^ 2({\mathbb{R}}^ n)\) for short range potentials V. We obtain classical determined asymptotic behavior of the quantum scattering operator applied to certain states of compact support. Our main result is the extension of a theorem of Yajima to the position representation. The techniques involve convolution with Gaussian states. The error terms are shown to have \(L^ 2\) norms of order \(\hslash^{-\epsilon}\) for arbitrarily small positive \(\epsilon\).

MSC:
35P25 Scattering theory for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
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