2007/02/28 by Francois Castella, François Castella, Thierry Jecko +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Bounded function #Coulomb #Electron #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Numerical methods in inverse problems #Operator (biology) #Physics #Quantum mechanics #Regularization (linguistics) #Resolvent #Schrödinger's cat #Semiclassical physics #Spectral Theory in Mathematical Physics #math-ph #math.FA #math.MP #msc:35J10 #msc:35S30 #msc:81U05
paper · pdf · doi:10.1007/s00023-008-0372-x
39 pages, no figures, corrected version
arxiv created 2007/12/20 · openalex publication_date 2008/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Consider the Schroedinger operator with semiclassical parameter h, in the limit where h goes to zero. When the involved long-range potential is smooth, it is well known that the boundary values of the operator's resolvent at a positive energy E are bounded by O(1/h) if and only if the associated Hamilton flow is non-trapping at energy E. In the present paper, we extend this result to the case where the potential may possess Coulomb singularities. Since the Hamilton flow then is not complete in general, our analysis requires the use of an appropriate regularization.