An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces

2005/10/25 by D.J. Rowe, D J Rowe, D. J. Rowe · 4 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Nuclear physics research studies #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/38/47/009

19 pages, 8 figures

arxiv created 2005/10/25 · openalex publication_date 2005/11/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given for SO(N)-reduced matrix elements of basic orbital observables. These developments make it possible to determine the matrix elements of polynomial and a other Hamiltonians analytically, to within SO(N) Clebsch-Gordan coefficients, and to select an optimal basis for a particular problem such that the expansion of eigenfunctions is most rapidly convergent.

Cited by

• Triaxial shapes in even-even nuclei: A theoretical overview
• The quadrupole collective model from a Cartan–Weyl perspective
• Euclidean dynamical symmetry in nuclear shape phase transitions
• Algebraic evaluation of matrix elements in the Laguerre function basis