Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes (Q1114139)

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.