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Il Nuovo Cimento A (1965-1970)

, Volume 61, Issue 4, pp 655–662 | Cite as

A remark on bound states in potential-scattering theory

  • D. Ruelle
Article

Summary

Let ℋ = ℋ B + ℋ C be the Hilbert space of ann-particle quantum system, where ℋ B is spanned by the bound states and ℋ C corresponds to the continuous spectrum of the Hamiltonian. It is shown that the wave functions which are in some sense localized in space and energy form a compact set in ℋ. This is used to prove that a wave packet ψ remains localized at finite distance for all time if ψ∈ℋ B , and that it disappears at infinity if ψ∈ℋ C .

Keywords

Wave Packet Compact Operator Negative Part Spectral Projection Relativistic Quantum Mechanic 
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.

Замечания о связанных состояниях в потенциальной теории рассеяния

Riassunto

Sia ℋ = ℋ B + ℋ C lo spazio hilbertiano di un sistema quantistico din particelle, in cui ℋ B è coperto dagli stati legati e ℋ C corrisponde allo spettro continuo dell'hamiltoniana. Si dimostra che le funzioni d'onda che sono in un certo senso localizzate nello spazio e nell'energia formano un insieme compatto in ℋ. Da ciò si dimostra che un pacchetto d'onde ψ rimane localizzato ad una distanza finita in tutti gli istanti se ψ∈ℋ B , e che scompare all'infinito se ψ∈ℋ C .

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Copyright information

© Società Italiana di Fisica 1969

Authors and Affiliations

  • D. Ruelle
    • 1
  1. 1.University of CaliforniaIrvine

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