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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Time Delay in Quantum Scattering

H. M. Nussenzveig

Published Sep 15, 1972• 42 citations
Publisher

Abstract

A new definition of the time delay in the scattering of a quantum-mechanical wave packet is proposed. It has a broader domain of applicability than previous definitions. The average time delay for the scattering of a plane-wave train is evaluated. Applications of the result to the quantum theory of the second virial coefficient are given.

DOI
10.1103/physrevd.6.1534

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•Jan 1, 2012•0 citations
A new definition of the time delay in the scattering of a quantum-mechanical wave packet is proposed. It has a broader domain of applicability than previous definitions. The average time delay for the scattering of a plane-wave train is evaluated. Applications of the result to the quantum theory of the second virial coefficient are given.
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.”
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 shouldn't be called "times".
The problem of time delay in quantum mechanics and its relation to the classical concept of traversal time is studied. For a monochromatic wave, in one dimension, it is shown that the time delay is proportional to a linear combination of the derivatives of the phases of the transmission and reflection coefficients with respect to the frequency. In particular it is shown that the definition of time delay for quantum coherence given in terms of the periods of oscillations of a wave packet between the two wells, in the proper limit, agrees with the corresponding definition in tunneling.
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.”