An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces
Mathematical Physics
2009-11-11 v1 math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0510086,
title = {An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces},
author = {D. J. Rowe},
journal= {arXiv preprint arXiv:math-ph/0510086},
year = {2009}
}
Comments
19 pages, 8 figures