Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Equivalence between time-dependent and time-independent formulations of time delay

D. Bollé, T. A. Osborn

Published Jun 15, 1975• 16 citations
Publisher

Abstract

The time-dependent and time-independent treatments of time delay in two-body scattering are discussed and shown to be completely equivalent. Further, we provide a careful discussion of the definition of time delay in both approaches. We are able to establish that the customary method of using an average limiting process is unnecessary if the time delay is evaluated between normalizable wave packets.

DOI
10.1103/physrevd.11.3417

Related papers

Time Delay for Wave Packets in Nonrelativistic Scattering Theory with Inelastic Channels Present

R. Fong

Time delay is considered in nonrelativistic scattering theory with two-particle inelastic channels present. A comparison method is discussed, which in turn leads to a more natural definition based on the classical definition of time delay for inelastic scattering.

Physical Review•Nov 8, 1965•5 citations

Generalized definition of time delay in scattering theory

Christian Gérard, Rafael Tiedra de Aldecoa

We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.

arXiv:math-ph/0609044•Journal of Mathematical Physics•Dec 1, 2007•15 citations

Time Delay in Quantum Scattering

H. M. Nussenzveig

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.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Sep 15, 1972•42 citations

Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition

Massimiliano Sassoli de Bianchi

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.”

arXiv:1010.5329•Open Physics•Dec 12, 2011•12 citations

Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition

Massimiliano Sassoli de Bianchi

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".

•Jan 1, 2012•12 citations

Two-Body Scattering with Wave Packets

C. L. Hammer, T. A. Weber

Two-body scattering is analyzed using a time-dependent formalism and wave packets of arbitrary shape as the initial wavefunctions. In particular, the case of single-channel resonant scattering is discussed in some detail. In addition to the usual amplitudes resulting from the potential term and the resonant term, a third amplitude is found which interferes with the other two. Another interesting result is that in this formalism the final state is not necessarily represented by spherical outgoing waves, but can be interpreted instead as two separate outgoing wave packets whose shape is different from the initial packets. The Wigner time delay is obtained as a natural consequence of the analysis, and the resonant cross sections are expressed as density matrices constructed from the wave packets.

Journal of Mathematical Physics•Mar 1, 1967•6 citations
The time-dependent and time-independent treatments of time delay in two-body scattering are discussed and shown to be completely equivalent. Further, we provide a careful discussion of the definition of time delay in both approaches. We are able to establish that the customary method of using an average limiting process is unnecessary if the time delay is evaluated between normalizable wave packets.
We advocate for the systematic use of a symmetrized definition of time delay in scattering theory. In two-body scattering processes, we show that the symmetrized time delay exists for arbitrary dilated spatial regions symmetric with respect to the origin. It is equal to the usual time delay plus a new contribution, which vanishes in the case of spherical spatial regions. We also prove that the symmetrized time delay is invariant under an appropriate mapping of time reversal. These results are also discussed in the context of classical scattering theory.
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".
Two-body scattering is analyzed using a time-dependent formalism and wave packets of arbitrary shape as the initial wavefunctions. In particular, the case of single-channel resonant scattering is discussed in some detail. In addition to the usual amplitudes resulting from the potential term and the resonant term, a third amplitude is found which interferes with the other two. Another interesting result is that in this formalism the final state is not necessarily represented by spherical outgoing waves, but can be interpreted instead as two separate outgoing wave packets whose shape is different from the initial packets. The Wigner time delay is obtained as a natural consequence of the analysis, and the resonant cross sections are expressed as density matrices constructed from the wave packets.