J-matrix method of scattering in one dimension: The nonrelativistic theory

A. D. Alhaidari; H. Bahlouli; M. S. Abdelmonem

doi:10.1016/j.aop.2009.08.001

J-matrix method of scattering in one dimension: The nonrelativistic theory

A. D. Alhaidari^*, H. Bahlouli, M. S. Abdelmonem

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.

Original language	English
Pages (from-to)	2561-2578
Number of pages	18
Journal	Annals of Physics
Volume	324
Issue number	12
DOIs	https://doi.org/10.1016/j.aop.2009.08.001
State	Published - Dec 2009

Bibliographical note

Funding Information:
Partial support of this work by King Fahd University of Petroleum and Minerals under project SB-090001 is deeply appreciated. The financial support by the Saudi Center for Theoretical Physics (SCTP) is highly acknowledged.

Keywords

J-matrix
One dimension
Phase shift
Recursion relation
Reflection
Scattering
Transmission
Tridiagonal physics

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1016/j.aop.2009.08.001

Cite this

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title = "J-matrix method of scattering in one dimension: The nonrelativistic theory",

abstract = "We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.",

keywords = "J-matrix, One dimension, Phase shift, Recursion relation, Reflection, Scattering, Transmission, Tridiagonal physics",

author = "Alhaidari, \{A. D.\} and H. Bahlouli and Abdelmonem, \{M. S.\}",

note = "Funding Information: Partial support of this work by King Fahd University of Petroleum and Minerals under project SB-090001 is deeply appreciated. The financial support by the Saudi Center for Theoretical Physics (SCTP) is highly acknowledged. ",

year = "2009",

month = dec,

doi = "10.1016/j.aop.2009.08.001",

language = "English",

volume = "324",

pages = "2561--2578",

journal = "Annals of Physics",

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TY - JOUR

T1 - J-matrix method of scattering in one dimension

T2 - The nonrelativistic theory

AU - Alhaidari, A. D.

AU - Bahlouli, H.

AU - Abdelmonem, M. S.

N1 - Funding Information: Partial support of this work by King Fahd University of Petroleum and Minerals under project SB-090001 is deeply appreciated. The financial support by the Saudi Center for Theoretical Physics (SCTP) is highly acknowledged.

PY - 2009/12

Y1 - 2009/12

N2 - We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.

AB - We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.

KW - J-matrix

KW - One dimension

KW - Phase shift

KW - Recursion relation

KW - Reflection

KW - Scattering

KW - Transmission

KW - Tridiagonal physics

UR - https://www.scopus.com/pages/publications/70350705847

U2 - 10.1016/j.aop.2009.08.001

DO - 10.1016/j.aop.2009.08.001

M3 - Article

AN - SCOPUS:70350705847

SN - 0003-4916

VL - 324

SP - 2561

EP - 2578

JO - Annals of Physics

JF - Annals of Physics

IS - 12

ER -

J-matrix method of scattering in one dimension: The nonrelativistic theory

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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