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V. Weisskopf andE. Wigner:Zeits. Phys.,63, 54 (1930).
The decay law deviations in the context of radiation damping theory are discussed briefly inM. N. Hack andM. Hamermesh:Nuovo Cimento,19, 546 (1961) andM. N. Hack:Nuovo Cimento,22, 168 (1961).
For a different treatment, seeW. R. Frazer andS. Peyton:Ann. of Phys.,40, 46 (1966) andE. J. Hellund:Phys. Rev.,89, 919 (1953).
We suppose a cut-off introduced, if necessary, to insure that the Hamiltonian is a well-defined self-adjoint operator. The assertion then follows from Stone’s theorem (see,e.g.,F. Riesz andB. Szent-Nagy:Functional Analysis (New York, 1955), pp. 384–385).
This holds whenΓ ≪ ωo,i.e., lifetime much longer than characteristic period. Cf.,e.g., ref. (2).
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Hack, M.N. Basis for the departure from exponential decay. Nuovo Cimento B (1965-1970) 47, 301–302 (1967). https://doi.org/10.1007/BF02710733
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DOI: https://doi.org/10.1007/BF02710733