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Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes. (English) Zbl 0663.47009
The authors study the semiclassical asymptotics (h\(\to 0)\) for local spectral densities of Schrödinger operators \(H(h)=-h^ 2\Delta +V\) in \({\mathbb{R}}^ n\), \(n\geq 2\). For a class of central potentials it is shown that the local spectral density converges to the corresponding quantity in a stronger sense than proved in previous papers if the energy is restricted to a certain “non-trapping” region. As a consequence the authors proved the convergence of the quantum time delay to its classical value in the non-trapping region.
Reviewer: R.Alicki

MSC:
47A40 Scattering theory of linear operators
34L99 Ordinary differential operators
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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