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


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 .


Wave Packet Compact Operator Negative Part Spectral Projection Relativistic Quantum Mechanic 
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Замечания о связанных состояниях в потенциальной теории рассеяния


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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