2010
DOI: 10.1143/ptps.184.516
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Replacing the Breit-Wigner Amplitude by the Complex Delta Function to Describe Resonances

Abstract: Whenever the Breit-Wigner amplitude appears in a calculation, there are many instances (e.g., Fermi's two-level system and the Weisskopf-Wigner approximation) where energy integrations are extended from the scattering spectrum of the Hamiltonian to the whole real line. Such extensions are performed in order to obtain a desirable, causal result. In this paper, we recall several of those instances and show that substituting the Breit-Wigner amplitude by the complex delta function allows us to recover such desira… Show more

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“…One of the earliest and most-studied appraoches involves the construction of an arrival time operator [6] by quantizing the classical result −mx/p (for an incoming classical particle with momentum p and position x). This typically leads to arrival time operators which are not self-adjoint [7], although self-adjoint variants have been proposed [8][9][10]. Even when self-adjoint, such operators are not obviously connected to a particular measurement scheme, since there is no obvious way of creating a physically realizable coupling between a measuring device and any of the proposed arrival time operators.…”
Section: Introductionmentioning
confidence: 99%
“…One of the earliest and most-studied appraoches involves the construction of an arrival time operator [6] by quantizing the classical result −mx/p (for an incoming classical particle with momentum p and position x). This typically leads to arrival time operators which are not self-adjoint [7], although self-adjoint variants have been proposed [8][9][10]. Even when self-adjoint, such operators are not obviously connected to a particular measurement scheme, since there is no obvious way of creating a physically realizable coupling between a measuring device and any of the proposed arrival time operators.…”
Section: Introductionmentioning
confidence: 99%