Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta

Klaus Schulten, Roy G. Gordon

Research output: Contribution to journalReview article

Abstract

Algorithms are developed for the exact evaluation of the By-coefficients of Wigner and the 6j-coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.

Original languageEnglish (US)
Pages (from-to)1961-1970
Number of pages10
JournalJournal of Mathematical Physics
Volume16
Issue number10
StatePublished - Dec 1 1974

Fingerprint

Angular momentum
Angular Momentum
angular momentum
evaluation
Quantum theory
Convergence of numerical methods
Evaluation
Coefficient
coefficients
numerical stability
Recursion Relations
Numerical Stability
Quantum Theory
quantum theory
Summation
quantum numbers
Exact Solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta. / Schulten, Klaus; Gordon, Roy G.

In: Journal of Mathematical Physics, Vol. 16, No. 10, 01.12.1974, p. 1961-1970.

Research output: Contribution to journalReview article

@article{caf5de267383455d9fde4e198e773a97,
title = "Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta",
abstract = "Algorithms are developed for the exact evaluation of the By-coefficients of Wigner and the 6j-coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.",
author = "Klaus Schulten and Gordon, {Roy G.}",
year = "1974",
month = "12",
day = "1",
language = "English (US)",
volume = "16",
pages = "1961--1970",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "10",

}

TY - JOUR

T1 - Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta

AU - Schulten, Klaus

AU - Gordon, Roy G.

PY - 1974/12/1

Y1 - 1974/12/1

N2 - Algorithms are developed for the exact evaluation of the By-coefficients of Wigner and the 6j-coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.

AB - Algorithms are developed for the exact evaluation of the By-coefficients of Wigner and the 6j-coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.

UR - http://www.scopus.com/inward/record.url?scp=36749112519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749112519&partnerID=8YFLogxK

M3 - Review article

AN - SCOPUS:36749112519

VL - 16

SP - 1961

EP - 1970

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

ER -