Torus quantization for spinning particles

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].

4 pages, 1 figure

References in corpus (4)

• A semiclassical approach to the Dirac equation
• Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
• Semiclassical form factor for chaotic systems with spin 1/2
• Quantum and classical ergodicity of spinning particles

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