Physics – Atomic and Molecular Clusters
Scientific paper
1999-05-27
J. Phys. B vol. 32 (28 March 1999) R1-R37
Physics
Atomic and Molecular Clusters
37 pages, 2 eps figures
Scientific paper
10.1088/0953-4075/32/6/004
The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions democratically, as a set of angles orthogonal to this collective radius or by equivalent variables, bypasses all independent-particle approximations. The invariance of the total kinetic energy under arbitrary d-dimensional transformations which preserve the radial parameter gives rise to novel quantum numbers and ladder operators interconnecting its eigenstates at each value of the radial parameter. We develop the systematics and technology of this approach, introducing the relevant mathematics tutorially, by analogy to the familiar theory of angular momentum in three dimensions. The angular basis functions so obtained are treated in a manifestly coordinate-free manner, thus serving as a flexible generalized basis for carrying out detailed studies of wavefunction evolution in multi-particle systems.
Bohn John. L.
Fano Ugo
Green Daniel
Heim T. A.
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