Displaying similar documents to “A generalization of the radiation condition of Sommerfeld for N -body Schrödinger operators”

Propagation of singularities in many-body scattering in the presence of bound states

András Vasy (1999)

Journées équations aux dérivées partielles

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In these lecture notes we describe the propagation of singularities of tempered distributional solutions u ∈ 𝒮 ' of ( H - λ ) u = 0 , where H is a many-body hamiltonian H = Δ + V , Δ ≥ 0 , V = ∑ a V a , and λ is not a threshold of H , under the assumption that the inter-particle (e.g. two-body) interactions V a are real-valued polyhomogeneous symbols of order - 1 (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is...