A generalization of the radiation condition of Sommerfeld for $N$-body Schrödinger operators

Hiroshi Isozaki

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In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u \in 𝒮^{'}$ of $(H - λ) u = 0$ , where $H$ is a many-body hamiltonian $H = Δ + V$ , $Δ \geq 0$ , $V = \sum_{a} V_{a}$ , 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...

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

Semiclassical resolvent estimates for two and three-body Schrödinger operators

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New channels in three-body long-range scattering

Radiation conditions and scattering theory for N -particle quantum systems

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

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

Radiation conditions and scattering theory for $N$ -particle quantum systems

Radiation conditions and scattering theory for $N$ -particle hamiltonians (main ideas of the approach)