Torus quantization for spinning particles

Details Torus quantization for spinning particles Torus quantization for spinning particles

2002-07-17

arxiv.org/abs/quant-ph/0207095v1

Phys. Rev. Lett. 89 (2002) 210405

Physics

Quantum Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.89.210405

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].

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