dorsal/arxiv
View SchemaGeometry and symmetries of multi-particle systems
| Authors | U. Fano, D. Green, J. L. Bohn, T. A. Heim |
|---|---|
| Categories | |
| ArXiv ID | physics/9905052 |
| URL | https://arxiv.org/abs/physics/9905052 |
| DOI | 10.1088/0953-4075/32/6/004 |
| Journal | J. Phys. B vol. 32 (28 March 1999) R1-R37 |
Abstract
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.
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"abstract": "The quantum dynamical evolution of atomic and molecular aggregates, from\ntheir compact to their fragmented states, is parametrized by a single\ncollective radial parameter. Treating all the remaining particle coordinates in\nd dimensions democratically, as a set of angles orthogonal to this collective\nradius or by equivalent variables, bypasses all independent-particle\napproximations. The invariance of the total kinetic energy under arbitrary\nd-dimensional transformations which preserve the radial parameter gives rise to\nnovel quantum numbers and ladder operators interconnecting its eigenstates at\neach value of the radial parameter.\n We develop the systematics and technology of this approach, introducing the\nrelevant mathematics tutorially, by analogy to the familiar theory of angular\nmomentum in three dimensions. The angular basis functions so obtained are\ntreated in a manifestly coordinate-free manner, thus serving as a flexible\ngeneralized basis for carrying out detailed studies of wavefunction evolution\nin multi-particle systems.",
"arxiv_id": "physics/9905052",
"authors": [
"U. Fano",
"D. Green",
"J. L. Bohn",
"T. A. Heim"
],
"categories": [
"physics.atm-clus",
"nucl-th"
],
"doi": "10.1088/0953-4075/32/6/004",
"journal_ref": "J. Phys. B vol. 32 (28 March 1999) R1-R37",
"title": "Geometry and symmetries of multi-particle systems",
"url": "https://arxiv.org/abs/physics/9905052"
},
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