J Shanghai Jiaotong Univ Sci

Journal of Shanghai Jiao Tong University (Science) ›› 2018, Vol. 23 ›› Issue (1): 146-157.doi: 10.1007/s12204-018-1920-2

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Focal Points at Infinity for Short-Range Scattering Trajectories

Focal Points at Infinity for Short-Range Scattering Trajectories

HOHBERGER Horst1*, KLEIN Markus2*   

  1. (1. University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China; 2. Institute for Mathematics, University of Potsdam, Potsdam 14476, Germany)
  2. (1. University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China; 2. Institute for Mathematics, University of Potsdam, Potsdam 14476, Germany)
  • Online:2018-02-01 Published:2018-02-01
  • Contact: HOHBERGER Horst, KLEIN Markus E-mail:horst@sjtu.edu.cn; mklein@math.uni-potsdam.de

Abstract: Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of that manifold.

Key words: Lagrangian manifold| classical scattering theory| short-range potential

摘要： Classical scattering trajectories are known to form a Lagrangian manifold in euclidean phase space, which allows the classification of local focal points for sufficiently small dimensions. For the case of a short-range potential, we show that the natural description of focal points at infinity is a Lagrangian manifold in the cotangent bundle of the sphere and establish the relationship between focal points at infinity and the projection singularities of that manifold.

关键词: Lagrangian manifold| classical scattering theory| short-range potential

CLC Number: