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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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##### References:
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