|
| related topics |
| {equation, function, exp} |
| {field, particle, equation} |
| {group, space, representation} |
| {phase, path, phys} |
| {classical, space, random} |
| {let, theorem, proof} |
| {spin, pulse, spins} |
| {cos, sin, state} |
|
Torus quantization for spinning particles
Stefan Keppeler
abstract: We derive semiclassical quantization conditions for systems with spin. To
this end one has to define the notion of integrability for the corresponding
classical system which is given by a combination of the translational motion
and classical spin precession. We determine the geometry of the invariant
manifolds of this product dynamics which support semiclassical solutions of the
wave equation. The semiclassical quantization conditions contain a new term,
which is of the same order as the Maslov correction. This term is identified as
a rotation angle for a classical spin vector. Applied to the relativistic
Kepler problem the procedure sheds some light on the amazing success of
Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1-94].
- oai_identifier:
- oai:arXiv.org:quant-ph/0207095
- categories:
- quant-ph math-ph math.MP nlin.CD
- comments:
- 4 pages, 1 figure
- doi:
- 10.1103/PhysRevLett.89.210405
- arxiv_id:
- quant-ph/0207095
- journal_ref:
- Phys. Rev. Lett. 89 (2002) 210405
- report_no:
- ULM-TP/02-5
- created:
- 2002-07-17
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