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

Journal of Contemporary Physics (Armenian Academy of Sciences)

Multichannel scattering amplitudes of microparticles in a quantum well with two-dimensional δ-potential

Д. М. Седракян, D. H. Badalyan, Л. Р. Седракян

Published Apr 1, 2015• 4 citations
Publisher

Abstract

The quasi-one-dimensional scattering of a quantum particle on the two-dimensional δ-potential is considered. Analytical expressions for multi-channel transmission t n and reflection r n amplitudes are given. The problem is solved for the case of finite number of channels that is equal to N when the particle is incident on the potential while moving in l channel. The case of three-channel scattering was examined in details. As was shown within the frameworks of this problem, the “overpopulation” of particles in the second and third channels occurs when k 2 → 0 and k 3 → 0. The location points of δ-potential that provide the complete “overpopulation” of channels were also obtained.

DOI
10.3103/s1068337215020048

Related papers

Amplitudes of two-channel scattering by a two-dimensional potential barrier with a constant height

Д. М. Седракян, Eduard M Kazaryan, Л. Р. Седракян

The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t 1, t 2, r 1, and r 2 are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k 2 → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.

Journal of Contemporary Physics (Armenian Academy of Sciences)•Apr 29, 2010•5 citations

Amplitudes of multichannel scattering on a two-dimensional potential barrier with constant height

Д. М. Седракян, Л. Р. Седракян, A. V. Margaryan

The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t m and r m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ™-potential is performed. For this case transmission amplitudes t m and reflection amplitudes r m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.

Journal of Contemporary Physics (Armenian Academy of Sciences)•May 4, 2011•1 citation

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

Д. М. Седракян, Л. Р. Седракян

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t m and r m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t m and reflection amplitudes r m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k l corresponding to the channel l.

Journal of Contemporary Physics (Armenian Academy of Sciences)•Aug 21, 2014•1 citation

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

Д. М. Седракян, Eduard M Kazaryan, Л. Р. Седракян

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T i and reflection R i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T 1, T 2 and R 1, R 2 is proposed.

Journal of Contemporary Physics (Armenian Academy of Sciences)•Jan 7, 2011•3 citations

Scattering by a finite periodic potential

Donald W. L. Sprung, Hua Wu, Joan Martorell

The problem of scattering in one dimension by a potential which consists of N identical cells is solved in a transparent manner. The N-cell transmission and reflection amplitudes are expressed in terms of the single-cell amplitudes and the Bloch phase. As examples the results are applied to a row of delta-function potentials, and to a row of square wells, and it is shown that these expressions provide an immediate understanding of the results of detailed calculations.

American Journal of Physics•Dec 1, 1993•169 citations

Analytical properties of scattering amplitudes in one-dimensional quantum theory

M. S. Marinov, Segev, B

One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The transition and reflection amplitudes are expressed in terms of two complex functions of the incident energy, which are similar to the Jost function in the partial-wave scattering. These functions are entire for finite-range potentials and meromorphic for exponentially decreasing potentials. The analytical properties result from locality of the potential in the wave equation and represent the effect of causality in time dependence of the scattering process.

•Feb 20, 1996•17 citations
The quasi-one-dimensional scattering of a quantum particle on the two-dimensional δ-potential is considered. Analytical expressions for multi-channel transmission t n and reflection r n amplitudes are given. The problem is solved for the case of finite number of channels that is equal to N when the particle is incident on the potential while moving in l channel. The case of three-channel scattering was examined in details. As was shown within the frameworks of this problem, the “overpopulation” of particles in the second and third channels occurs when k 2 → 0 and k 3 → 0. The location points of δ-potential that provide the complete “overpopulation” of channels were also obtained.
The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t 1, t 2, r 1, and r 2 are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k 2 → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.
The immersing method is applied to solve the N-channel scattering problem for concrete potential. In particular, we consider the particle scattering on a two-dimensional potential barrier, which is constant in the scattering direction and arbitrary in the cross-section direction. For this case the scattering amplitudes t m and r m (1,2, m= ...,N) are determined. A transition from the obtained formulas to the case of ™-potential is performed. For this case transmission amplitudes t m and reflection amplitudes r m are obtained. It is also shown that the product of transmission and reflection amplitudes along the channel m does not depend on the scattering channel.
The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t m and r m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t m and reflection amplitudes r m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k l corresponding to the channel l.
The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T i and reflection R i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T 1, T 2 and R 1, R 2 is proposed.
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The transition and reflection amplitudes are expressed in terms of two complex functions of the incident energy, which are similar to the Jost function in the partial-wave scattering. These functions are entire for finite-range potentials and meromorphic for exponentially decreasing potentials. The analytical properties result from locality of the potential in the wave equation and represent the effect of causality in time dependence of the scattering process.