Abstract
The formulation of quantum mechanics in rigged Hilbert spaces is used to study the vector states for resonance states or Gamow vectors. An important part of the work is devoted to the construction of Gamow vectors for resonances that appear as multiple poles on the analytic continuation of theS-matrix,S(E). The kinematical behavior of these vectors is also studied. This construction allow for generalized spectral decompositions of the Hamiltonian and the evolutionary semigroups, valid on certain locally convex spaces. Also a first attempt is made to define the resonance states as densities in an extension of the Liouville space, here called rigged Liouville space.
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Gadella, M. Vector states for single and multiple-pole resonances. Int J Theor Phys 36, 2271–2294 (1997). https://doi.org/10.1007/BF02768925
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DOI: https://doi.org/10.1007/BF02768925