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

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Relations between hyperspherical and harmonic-oscillator many-body matrix elements

Decio Levi B, M. Moshińsky

Published Mar 1, 1974• 9 citations
Publisher
DOI
10.1007/bf02727440

Related papers

Matrix Elements for the Harmonic Oscillator

Elsevier eBooks•Jan 1, 2002•0 citations

Matrix elements of potentials forL=1 hyperspherical states

Nir Barnea, Victor B. Mandelzweig

Three-body L=1 symmetrized hyperspherical harmonic functions, realizing irreducible representations of the permutation group of three particles, are expressed in terms of Wigner D functions. Matrix elements of arbitrary two-body potentials between these hyperspherical states, including their velocity-dependent parts, are calculated analytically and expressed through the sum of products of the Wigner 3-j symbols and explicitly written functions of the radial variable.

Physical Review A•May 1, 1990•29 citations

TRANSFER MATRICES IN QUANTUM MANY-BODY SYSTEMS

Tohru Koma

WORLD SCIENTIFIC eBooks•Dec 1, 1993•1 citation

Matrix elements between vector hyperspherical states

Nir Barnea, Victor B. Mandelzweig

Three-body symmetrized vector hyperspherical harmonic functions, realizing irreducible representations of the permutation group of three particles, are constructed and expressed in terms of Wigner D functions. Matrix elements of arbitrary two-body potentials between these hyperspherical states, including their velocity-dependent parts, are calculated analytically and expressed through the sum of products of the Wigner 3-j symbols and explicitly written functions of the radial variable.

Physical Review A•Dec 1, 1991•12 citations

Dynamics of quantum many-body systems with long-range interactions

Anton S. Buyskikh

•Jan 1, 2017•0 citations

Matrix elements of two-body operators between many-body symmetrized hyperspherical states

Akiva Novoselsky, Nir Barnea

Matrix elements of two-body operators between many-particle permutational symmetry-adapted functions in hyperspherical coordinates are constructed. The matrix elements are evaluated using the appropriate hyperspherical coefficients of fractional parentage, the Raynal-Revai coefficients, and the hyperspherical recoupling coefficients. We use the power expansion of the two-body operators and obtain an analytic expression for the matrix element of each term. These expressions are studied numerically. The results allow precise evaluations of two-body matrix elements for few-body calculations in nuclear, atomic, and molecular physics.

Physical Review A•Apr 1, 1995•17 citations
Matrix elements of two-body operators between many-particle permutational symmetry-adapted functions in hyperspherical coordinates are constructed. The matrix elements are evaluated using the appropriate hyperspherical coefficients of fractional parentage, the Raynal-Revai coefficients, and the hyperspherical recoupling coefficients. We use the power expansion of the two-body operators and obtain an analytic expression for the matrix element of each term. These expressions are studied numerically. The results allow precise evaluations of two-body matrix elements for few-body calculations in nuclear, atomic, and molecular physics.