Clebsch-Gordan coefficients and Racah coefficients for the SU(2) and SU(1,1) groups as the discrete analogues of the Poschl-Teller potential wavefunctions

Yu F. Smirnov, Sergei Suslov, A. M. Shirokov

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21 Citations (Scopus)

Abstract

The Clebsch-Gordan coefficients (CGC) and the Racah coefficients for the SU(2) and SU(1,1) groups are studied as functions of a discrete variable. It has been shown that CGC for SU(2) and SU(1,1) groups may be considered to be discrete analogues of wavefunctions for the one-dimensional Schrodinger equation with the Poschl-Teller potential. Expressions for CGC and 6j-symbols of the SU(1,1) group have been found through the Hahn and Racah polynomials. Consideration is given to the asymptotic properties of eigenvalues and eigenfunctions of the Hamiltonian of an asymmetric top and of the Bargmann-Moshinsky operator Omega.

Original languageEnglish (US)
Article number013
Pages (from-to)2157-2175
Number of pages19
JournalJournal of Physics A: Mathematical and General
Volume17
Issue number11
DOIs
StatePublished - 1984
Externally publishedYes

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Racah coefficient
Clebsch-Gordan coefficients
Schrodinger equation
Hamiltonians
Wave functions
Eigenvalues and eigenfunctions
Polynomials
analogs
Analogue
Coefficient
coefficients
asymptotic properties
Schrodinger Equation
Discrete Variables
Eigenvalues and Eigenfunctions
eigenvectors
polynomials
eigenvalues
Asymptotic Properties
operators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

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abstract = "The Clebsch-Gordan coefficients (CGC) and the Racah coefficients for the SU(2) and SU(1,1) groups are studied as functions of a discrete variable. It has been shown that CGC for SU(2) and SU(1,1) groups may be considered to be discrete analogues of wavefunctions for the one-dimensional Schrodinger equation with the Poschl-Teller potential. Expressions for CGC and 6j-symbols of the SU(1,1) group have been found through the Hahn and Racah polynomials. Consideration is given to the asymptotic properties of eigenvalues and eigenfunctions of the Hamiltonian of an asymmetric top and of the Bargmann-Moshinsky operator Omega.",
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