A REMARK ON BOUND STATES IN POTENTIAL-SCATTERING THEORY

Let ℋ = ℋ B + ℋ C be the Hilbert space of an n-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 . © 1969 Società Italiana di Fisica.