A band factorization technique for transition matrix element asymptotics

Emmanuel Perrey-Debain; I. David Abrahams

doi:10.1016/j.cpc.2006.05.003

A band factorization technique for transition matrix element asymptotics

Emmanuel Perrey-Debain, I. David Abrahams

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

Abstract

A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	315-322
Number of pages	7
Journal	Computer Physics Communications
Volume	175
Issue number	5
DOIs	https://doi.org/10.1016/j.cpc.2006.05.003
Publication status	Published - 1 Sept 2006

Keywords

Harmonic oscillator
Orthogonal polynomial
Quasi-classical approximation
Transition matrix

Access to Document

10.1016/j.cpc.2006.05.003

Cite this

@article{c2c9c44943f048419feb4d8f814c85ba,

title = "A band factorization technique for transition matrix element asymptotics",

abstract = "A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

keywords = "Harmonic oscillator, Orthogonal polynomial, Quasi-classical approximation, Transition matrix",

author = "Emmanuel Perrey-Debain and Abrahams, {I. David}",

year = "2006",

month = sep,

day = "1",

doi = "10.1016/j.cpc.2006.05.003",

language = "English",

volume = "175",

pages = "315--322",

journal = "Computer Physics Communications",

publisher = "Elsevier BV",

number = "5",

}

TY - JOUR

T1 - A band factorization technique for transition matrix element asymptotics

AU - Perrey-Debain, Emmanuel

AU - Abrahams, I. David

PY - 2006/9/1

Y1 - 2006/9/1

N2 - A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols. © 2006 Elsevier B.V. All rights reserved.

AB - A new method of evaluating transition matrix elements between wave functions associated with orthogonal polynomials is proposed. The technique relies on purely algebraic manipulation of the associated recurrence coefficients. The form of the matrix elements is perfectly suited to very large quantum number calculations by using asymptotic series expansions. In practice, this allows the accurate and fast numerical treatment of transition matrix elements in the quasi-classical limit. Examples include the matrix elements of xp in the harmonic oscillator basis, and connections with the Wigner 3j symbols. © 2006 Elsevier B.V. All rights reserved.

KW - Harmonic oscillator

KW - Orthogonal polynomial

KW - Quasi-classical approximation

KW - Transition matrix

U2 - 10.1016/j.cpc.2006.05.003

DO - 10.1016/j.cpc.2006.05.003

M3 - Article

VL - 175

SP - 315

EP - 322

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 5

ER -

A band factorization technique for transition matrix element asymptotics

Abstract

Keywords

Access to Document

Fingerprint

Cite this