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Quantum 2-Body Hamiltonians

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Abstract

In this chapter we study scattering theory for quantum time-independent 2-particle systems. They are described by Hamiltonians on L 2 (X) of the form

$$H = \frac{1}{2}{D^2} + V(x),$$
(4.0.1)

where V(x) decays in space in all directions. The previous chapter was devoted to Hamiltonians with time-decaying potentials and should be viewed as an introduction to the present one. In particular, various objects related to long-range scattering theory were discussed in Chap. 3. Therefore we advise the reader to first become familiar with the previous chapter, in particular with Sects. 3.2, 3.3 and 3.5.

Keywords

  • Wave Operator
  • Eikonal Equation
  • Fourier Integral Operator
  • Asymptotic Completeness
  • Joint Spectrum

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1997 Springer-Verlag Berlin Heidelberg

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Dereziński, J., Gérard, C. (1997). Quantum 2-Body Hamiltonians. In: Scattering Theory of Classical and Quantum N-Particle Systems. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03403-3_5

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  • DOI: https://doi.org/10.1007/978-3-662-03403-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08284-9

  • Online ISBN: 978-3-662-03403-3

  • eBook Packages: Springer Book Archive