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Annalen der Physik

Eine operative Definition des Begriffs der Streuverzögerung

Hanns Georg Kilian

Published Jan 1, 1968• 6 citations
Publisher

Abstract

Abstract We propose and discuss an operative definition of the notion of a mean collision time delay within the frame of non‐relativistic time‐dependent quantum scattering theory. As an application we calculate the collision time delay for two simple but interesting examples which permit us to make a preliminary calculation of the lifetime of a decaying compound system.

DOI
10.1002/andp.19684760504

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arXiv:0903.1823•Mar 10, 2009•0 citations
Abstract We propose and discuss an operative definition of the notion of a mean collision time delay within the frame of non‐relativistic time‐dependent quantum scattering theory. As an application we calculate the collision time delay for two simple but interesting examples which permit us to make a preliminary calculation of the lifetime of a decaying compound system.
Abstract We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”
The notion of time duration is considered within the framework of SSS-matrix theory. It is shown that Wigner's definition of the time delay, $\ensuremath{-}i\ensuremath{\hbar}[(\frac{d\mathrm{ln}S}{\mathrm{dE}})]$, for a scattering process permits one to define time duration in a "coarse-grained" sense.
For temporal magnitudes describing, in details, processes of particles scattering for a long time at each necessity case a particular, ad hoc reception were used. However the desirability of general approach basing on concepts of quantum field theory and uniting two main problems, durations of delay at scattering and of formation of arisen states, seems evident. We show that the Ward-Takahashi identity allows the defining of general temporal function in the frame of QED, real part of which describes the duration of delay of scattered particle on scatterer and imaginary part describes the duration of formation ("dressing") of outgoing bare particle. The functions of same form can be revealed in the known QED descriptions of processes, i.e. they arise in the course of standard calculations, but are not entered artificially. These functions submit to the operator of duration determinable by the reciprocal analogue of the Schroedinger equation, operator of which is canonically conjugated with Hamiltonian. Definition of temporal functions leads to the developing of such kinetic theories: theory of optical dispersion (with the decision of certain known paradoxes), theory of multiphoton processes (definitions of their thresholds and saturations) and theory of phase transitions (determination of general correlation radii and the full system of critical indices). The determination of temporal functions demonstrates also the instanton-type nature of tunneling processes, makes clear sense of the adiabatic hypothesis of quantum theory and some renormalization schemes. In an application to the problem of charge nullification they lead to a restriction of allowable number of fermions of the theory.