Physical representations of Gamow states in a rigged Hilbert space

Bollini, C. G.; Civitarese, O.; Paoli, A. L. De; Rocca, M. C.

doi:10.1016/0370-2693(96)00685-5

Cited by 24 publications

(48 citation statements)

References 20 publications

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“…When he writes δ N (φ) as an integral operator, Nakanishi uses the following expression: 14) where 15) and where the contour γ is such that the integral in Eq. (B.14) decomposes into two terms.…”

Section: B3 Nakanishi's Definitionmentioning

confidence: 99%

The resonance amplitude associated with the Gamow states

Madrid

2008

Nuclear Physics A

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The Gamow states describe the quasinormal modes of quantum systems. It is shown that the resonance amplitude associated with the Gamow states is given by the complex delta function. It is also shown that under the near-resonance approximation of neglecting the lower bound of the energy, such resonance amplitude becomes the Breit-Wigner amplitude. This result establishes the precise connection between the Gamow states, Nakanishi's complex delta function and the Breit-Wigner amplitude. In addition, this result provides another theoretical basis for the phenomenological fact that the almost-Lorentzian peaks in cross sections are produced by intermediate, unstable particles.

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Section: B3 Nakanishi's Definitionmentioning

confidence: 99%

The resonance amplitude associated with the Gamow states

Madrid

2008

Nuclear Physics A

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“…In three previous papers [1,2,3] we have shown that Gamow-states [4] can be interpreted as Sebastiao e Silva's Ultradistributions [5,6,7], whose proper treatment appeals to Rigged Hilbert Space [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

q-Gamow states as continuous linear functionals on analytical test functions

Plastino

Rocca

2016

Nuclear Physics A

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“…It was shown in [5,6,7,8] that resonances, i.e. Gamow-states [9,10], can be seen as (Sebastiao e Silva's) Ultradistributions [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

q-Gamow states for intermediate energies

et al. 2016

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In a recent paper [Nuc. Phys. A 948, (2016) 19] we have demonstrated the possible existence of Tsallis' q-Gamow states. Now, accelerators' experimental evidence for Tsallis' distributions has been ascertained only at very high energies. Here, instead, we develop a different set of q-Gamow states for which the associated q-Breit-Wigner distribution could easily be found at intermediate energies, for which accelerators are available at many locations. In this context, it should be strongly emphasized [Physica A 388 (2009) 601] that, empirically, one never exactly and unambiguously "detects" pure Gaussians, but rather q-Gaussians. A prediction is made via Eq. 3.30.

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Physical representations of Gamow states in a rigged Hilbert space

Cited by 24 publications

References 20 publications

The resonance amplitude associated with the Gamow states

The resonance amplitude associated with the Gamow states

q-Gamow states as continuous linear functionals on analytical test functions

q-Gamow states for intermediate energies

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