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Collisions for the quantum Coulomb Hamiltonian

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Abstract

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.

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Authors and Affiliations

  1. Centre de Mathématiques, Ecole Polytechnique, F-91128, Palaiseau, Cedex, France

    C. Gérard

  2. Technische Universität Fachbereich Mathematik, Straße des 17 Juni, 135, 1000, Berlin, Federal Republic of Germany

    A. Knauf

Authors
  1. C. Gérard
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  2. A. Knauf
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Communicated by B. Simon

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Gérard, C., Knauf, A. Collisions for the quantum Coulomb Hamiltonian. Commun.Math. Phys. 143, 17–26 (1991). https://doi.org/10.1007/BF02100283

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  • DOI: https://doi.org/10.1007/BF02100283

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