An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces

Details An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces

2005-10-25

arxiv.org/abs/math-ph/0510086v1

Physics

Mathematical Physics

19 pages, 8 figures

Scientific paper

10.1088/0305-4470/38/47/009

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.

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