Robert, Didier Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics. (English) Zbl 0813.35073 J. Funct. Anal. 126, No. 1, 36-82 (1994). The main goal of this article is to compare two long-range perturbations of constant coefficients operators on \(\mathbb{R}^ n\) such that their difference is short range. Typical examples are semi-classical Schrödinger Hamiltonians such that the difference of the corresponding potentials is decreasing sufficiently rapidly at \(\infty\). In this context the average time-delay depending on the energy \(\lambda\) and on the semiclassical parameter \(h\) is well defined and the author studies its asymptotic behavior in the high-energy “régime” and in the semi- classical “régime”. Reviewer: B.Helffer (Paris) Cited in 1 ReviewCited in 27 Documents MSC: 35P25 Scattering theory for PDEs 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory 47F05 General theory of partial differential operators Keywords:high-energy regime; semi-classical regime; semi-classical Schrödinger Hamiltonians; average time-delay PDFBibTeX XMLCite \textit{D. Robert}, J. Funct. Anal. 126, No. 1, 36--82 (1994; Zbl 0813.35073) Full Text: DOI