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| related topics |
| {group, space, representation} |
| {cos, sin, state} |
| {equation, function, exp} |
| {phase, path, phys} |
| {classical, space, random} |
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Semiclassical analysis of Wigner $3j$-symbol
Vincenzo Aquilanti, Hal M. Haggard, Robert G. Littlejohn, Liang Yu
abstract: We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element
connecting eigenfunctions of a pair of integrable systems, obtained by lifting
the problem of the addition of angular momenta into the space of Schwinger's
oscillators. A novel element is the appearance of compact Lagrangian manifolds
that are not tori, due to the fact that the observables defining the quantum
states are noncommuting. These manifolds can be quantized by generalized
Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry
of the classical angular momentum vectors emerges in a clear manner. Efficient
methods for computing amplitude determinants in terms of Poisson brackets are
developed and illustrated.
- oai_identifier:
- oai:arXiv.org:quant-ph/0703104
- categories:
- quant-ph
- comments:
- 7 figure files
- doi:
- 10.1088/1751-8113/40/21/013
- arxiv_id:
- quant-ph/0703104
- created:
- 2007-03-13
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