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

Annalen der Physik

Zeitabhängige Resonanzstreuung eines dreidimensionalen Wellenpakets

Franz Kitzka

Published Jan 1, 1972• 0 citations
Publisher

Abstract

Abstract A three dimensional wave packet, scattered by a radial symmetric potential of finite range, is studied, especially for the case of resonance scattering. It is found that for the calculation of the differential resonance cross section the three dimensionality of the packet may be neglected in favour of its structure in the direction of propagation. This is correct also for cross sections measured by shortly opened counters, provided that the opening time is greater in its order of magnitude than a time interval characteristic for the spreading of the packet.

DOI
10.1002/andp.19724830110

Related papers

Quantum scattering of the wave-packet confined in anisotropic paraboloidal shell potential

Philip Jordan D. Blancas, Eric A. Galapon

The differential scattering cross sections of the wave-packet incident to the convex and concave paraboiloidal shells, each of which has an anisotropic factor, are calculated by solving the Schrodinger equation in paraboloidal coordinate system.

Proceedings of the Samahang Pisika ng Pilipinas•Oct 22, 2012•0 citations

General time-dependent formulation of quantum scattering theory

Stuart C. Althorpe

We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fern\'andez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering.

Physical Review A•Apr 2, 2004•18 citations

Potential Scattering of a Wave Packet

W. Edward Gettys

A wave-packet formalism is presented for obtaining the differential cross section for the elastic scattering of a single particle by a potential. The method avoids difficulties inherent in the more common formulations such as interference between incident and scattered waves, box normalization, and density of final states. The time sequence of events in the scattering process is pictured in an intuitively appealing manner. The initial form of the wave packet is specified explicitly, and the time development of the wave packet is determined from the time-translation operator. The asymptotic form of the wave packet is investigated after a sufficiently long time lapse, and the cross section is obtained from a calculation of particle flux densities.

American Journal of Physics•Jun 1, 1965•1 citation

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

Scattering Cross Section for a Beam of Wave Packets

Amnon Katz

The scattering cross section is evaluated for a beam of wave packets of almost arbitrary form. It is found that this cross section is the superposition of the cross sections of various plane waves, which make up the wave packet without interference. For wave packets of well-defined momentum, the usual rule that the scattering cross section is the absolute square of the scattering amplitude is regained.

Journal of Mathematical Physics•Oct 1, 1966•3 citations

Transmission and reflection times for scattering of wave packets off tunneling barriers

E. H. Hauge, J. P. Falck, Tor A. Fjeldly

The proper basis for the calculation of transmission and reflection times for wave packets scattered off arbitrary tunneling structures in one dimension is considered. With packets narrow in wave-number space, we demonstrate that the classic phase times are indeed correct to lowest order. Explicit, general expressions for the leading correction terms for finite wave packets are given. The physics associated with these corrections is discussed. We also consider the dwell time, as it is currently defined, and derive a general relation between this dwell time and the phase times. This relation shows when the dwell time can and cannot be used. Finally, we discuss wave packets transmitted from narrow resonances, and derive an explicit, exact formula for the tunneling time with resonance transmission from a symmetric double barrier. Comparison with earlier approximate results is made.

Physical review. B, Condensed matter•Sep 15, 1987•212 citations
Abstract A three dimensional wave packet, scattered by a radial symmetric potential of finite range, is studied, especially for the case of resonance scattering. It is found that for the calculation of the differential resonance cross section the three dimensionality of the packet may be neglected in favour of its structure in the direction of propagation. This is correct also for cross sections measured by shortly opened counters, provided that the opening time is greater in its order of magnitude than a time interval characteristic for the spreading of the packet.
We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fern\'andez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering.
A wave-packet formalism is presented for obtaining the differential cross section for the elastic scattering of a single particle by a potential. The method avoids difficulties inherent in the more common formulations such as interference between incident and scattered waves, box normalization, and density of final states. The time sequence of events in the scattering process is pictured in an intuitively appealing manner. The initial form of the wave packet is specified explicitly, and the time development of the wave packet is determined from the time-translation operator. The asymptotic form of the wave packet is investigated after a sufficiently long time lapse, and the cross section is obtained from a calculation of particle flux densities.
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.
The proper basis for the calculation of transmission and reflection times for wave packets scattered off arbitrary tunneling structures in one dimension is considered. With packets narrow in wave-number space, we demonstrate that the classic phase times are indeed correct to lowest order. Explicit, general expressions for the leading correction terms for finite wave packets are given. The physics associated with these corrections is discussed. We also consider the dwell time, as it is currently defined, and derive a general relation between this dwell time and the phase times. This relation shows when the dwell time can and cannot be used. Finally, we discuss wave packets transmitted from narrow resonances, and derive an explicit, exact formula for the tunneling time with resonance transmission from a symmetric double barrier. Comparison with earlier approximate results is made.